A SEMI-STRONG FORM EVALUATION OF THE EFFICIENCY OF
THE WHEAT FUTURES MARKET
by
Llewelyn Edward Jones
A thesis submitted in par~ial fulfillment
of the requirements for the degree
of
Master of Science
in
Applied Economics
MONTANA STATE UNIVERSITY
Bozeman, Montana
March 1988
ii
APPROVAL
of a thesis submitted by
Llewelyn Edward Jones
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and has been found to be satisfactory regarding content, English usage,
format, citations, bibliographic style, and consistency, and is ready
for submission to the College of Graduate Studies.
Date
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Approved for the Major Department
Date
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Approved for the College of Graduate Studies
Date
Graduate Dean
j
iii
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iv
ACKNOWLEDGMENTS
I
Dr.
would
like to express my appreciation to my committee
Jeffrey T. LaFrance, Dr. Ronald N. Johnson, and Dr. John
members,
M.
Marsh
for their patience and guidance during the course of this thesis.
Special thanks go to my parents,
Edward and Marjorie, and my wife,
Carole, whose love and support made possible the pursuit and
of my academic goals.
attainment
v
TABLE OF CONTENTS
Page
APPROVAL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
ii
STATEMENT OF PERMISSION TO USE.............................
iii
ACKNOWLEDGMENTS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
iv
TABLE OF CONTENTS..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
v
LIST OF TABLES.............................................
vii
LIST OF FIGURES............................................
viii
ABSTRACT................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
i
x
CHAPTER
1.
2.
INTRODUCTION .................................... .
I nt reduction ................................. .
Statement of the Problem ..................... .
Objectives ................................... .
2
3
REVIEW OF THE LITERATURE ........................ .
5
The Theory of Efficient Markets .............. .
Efficient Futures Market Research ............ .
Wheat Price Forecasting Models ............... .
General Autoregressive Integrated Moving
Average Modeling Theory ...................... .
Development of an Efficiency Test for the
Wheat Futures Market ......................... .
Data Availability and Requirements ........... .
3.
1
5
12
17
21
25
29
EMPIRICAL RESULTS ............................... .
31
Soft Red Winter Wheat ARIMA Model ............ .
Random Walk Model Results ................. .
ARIMA(3,0,3) Model Results ................ .
USDA Model Results ........................... .
31
31
40
50
Vi
TABLE OF CONTENTS-Continued
Page
Market Trader's Model Results.................
Predicting the PPI............................
Utilizing the ARIMA(3,0,3) Model..............
55
59
60
SUMMARY AND CONCLUSIONS .........................•
66
Summary.......................................
Cone 1us ions. . . • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . • .
Further Research..............................
66
69
70
BIBLIOGRAPHY...............................................
72
APPENDIX ....••................•.•....•.....•......... ·..•...
76
4.
vi i
LIST OF TABLES
Table
Page
1.
Price Predictions with a Random Walk Model ....... .
37
2.
Predictions Made by the Wheat Futures Market ..... .
38
3.
Autocorrelation Check of Residuals ............... .
44
4.
Price Predictions with an ARIMA(3,0,3) Model ..... .
48
5.
Price Predictions with Model (23) ................ .
53
6.
Price Predictions with the Market Trader's
Mode 1 ............................................ .
57
7.
PPI Predictions with a Random Walk Model ......... .
60
8.
Returns to Market Price Speculation Using
the ARIMA(3,0,3) Model ........................... .
63
Original Data Set ................................ .
11
9.
viii
LIST OF FIGURES
Figure
Page
Relationship Between Quarterly Prices and
Stocks-to-Use Ratio ............................. .
19
2.
Nominal and Real Cash Soft Red Winter Wheat ..... .
32
3.
Random Walk Model's Forecast versus Cash
Price ........................................... .
40
Wheat Futures Market's Forecast versus Cash
Price ........................................... .
41
5.
Autocorrelation Function (ACF) for Cash Wheat ....
42
6.
Partial Autocorrelation Function (PACF) for
Cash Wheat ...................................... .
43
ARIMA(3,0,3) Model's Forecast versus Cash
Price ................................... ·· .. ··.··
49
8.
USDA Model's Forecast versus cash Price ......... .
54
9.
Market Trader's Model's Forecast versus Cash
Price ........................................... .
58
1.
4.
7.
~
ix
ABSTRACT
Futures market efficiency is of concern to both market participants
and non-participants. The practical problem is that inefficient futures
markets can lead to resource allocation problems. The specific objective
of this study is to perform a Fama (1970) semi-strong efficiency test on
the Chicago Board of Trade's wheat futures market.
In this study, three wheat price prediction models are used as a
standard with which to compare, on the basis of root mean squared error
and bias, the futures market. One of the models, an autoregressive
integrated moving average model, succeeded in obtaining a semi-strong
efficiency rejection. Returns from speculating with the autoregressive
integrated moving average model are then examined to see if the
incremental returns are sufficiently large to cover all costs of
speculating.
A 19.5 percent after cost return was generated by
simulating speculation with this model. Since a risk premium is
expected when using unproven methods to forecast price, it was not
determined whether this return is large enough to compensate for the
risks involved.
The results of this study indicate that there exists a possibility
that the Chicago Board of Trade's wheat futures market is not allocating
resources efficiently, at least for the time frame examined and
efficiency definition chosen.
As to whether this detected ineff~ciency
is just an anomaly caused by the time frame examined, efficiency
definition chosen, or the examination method, little can be said. The
results of this test are only strictly interpreted relative to the
particular definition of efficiency and time period chosen, and are not
used to infer that the futures market can be replaced by a "more
efficient" m~rketing tool.
1
CHAPTER 1
INTRODUCTION
Introduction
This
study
offers a semi-strong test
of the
Chicago Board of Trade's wheat futures market.
compares
price
predictions with predictions made
market
squared
the
study
quarterly
autoregressive
integrated
United Stated Department of Agriculture (USDA),
trader's models.
error
by
of
Specifically, the
the Chicago Board of Trade's wheat futures markets
moving average (ARIMA),
and
efficiency
The basts for
CRMSE) and bias.
comparison
The approach follows
is
the
root
mean
format
set
forth by Leuthold and Hartman's (1979) analysis of the Chicago Board
of
Trade's hog futures market with the exception that the structural models
used
to
literature
forward
price
rather
than
predict in this study
explicitly
created
were
from
chosen
economic
from
the
analysis.
Choosing models from the literature allows conclusions about the forward
price
predicting
ability of commonly accepted
models
while
avoiding
questions of model specification validity.
Following
explicitly
Fama
tested
(1970,
p.
1),
the
definition
in this study is, "A market in
reflect available information is called efficient."
of
which
efficiency
prices
fully
This definition was
made testable by Fama (1970) and is the model of choice for studies such
as
these.
Upon completion of this study some conclusions
about
wheat
2
futures
market efficiency and model choice are reached for
the
period
1966 to 1986.
Statement of the Problem
Grain
production and export trade is of tremendous
the United States; the
and exports
futures
number
United States produces 141 of the world's
SOl of the world's grain trade (Cramer et
markets
play
importance
an integral part in this grain
grain
al., 1983).
The
trade
the
with
of contracts traded increasing fifteen fold from 1960
to
Presently, there are approximately 9000 contracts traded per day
1985).
to
The Chicago Board of Trade's wheat futures market
is
1985.
<Peck,
generally
considered the key grain futures market for two reasons: (1) the largest
volume
futures
of grain futures trading, approximately 75% of the
total
grain
trade, occurs on the Chicago Board of Trade; and (2) while
the
contracts tendered on the Chicago Board of Trade are for soft red winter
wheat,
other grain varieties such as soft white wheat, hard red
wheat,
and
hard red spring wheat are accepted for
delivery
winter
with
the
appropriate premiums and discounts.
The
above
statements
plays
demonstrate the prominent role
in the United States
economy.
that
grain
futures
trading
A question
of
concern
to participants in this market is whether or not this market is
operating efficiently since an inefficient market could potentially lead
to
the misallocation of resources.
individuals
market,
but
that
still
may
use
This question is also important
not directly participate in
the wheat
function to make decisions.
futures
the
market's
to
wheat
futures
forward
pricing
3
The procedure for testing a market for pricing efficiency must take
into
consideration
chosen
for
futures
the
comparison.
trader's
cost and availability of any models
that
are
For
USDA
and
models
reason,
readily available
were selected and
deliberately kept simple.
hypothetical
thi~
modeling
procedures
Upon selection of a "best"
competing
trading with relevant commission charges will be
were
model,
executed
over a prospective test period.
Objectives
The specific objectives of this research project are:
1.
To test the hypothesis that the Chicago Board
of
Trade's
wheat futures market is efficient.
2.
To
rank, on the basis of RMSE and bias, USDA,
ARMA,
and
rejecting
the
futures trader's models.
3.
To
test
any
hypothesis
model(s) that succeed(s) in
in
objective (1) for after
commission
above
average returns where above average returns are defined to
be
returns
investments
Organization
reviews
previous
summarizes
develops
modeling,
definition
wheat
the
and
of
in
excess
of
the
return
such as cash deposits (CDs) at
this
thesis is as follows:
research
done on
futures
models that are present in
theory
rate
the
second
and
of efficiency.
a
testable
implication
from
chapter
efficiency,
literature,
behind autoregressive integrated
develops
"safe"
a bank.
markets
the
of
briefly
moving
average
the
chosen
Chapter 3 presents the empirical results
of
4
the
efficiency
tests
undertaken.
Chapter
4
includes
the
suggestions for further research, and other concluding remarks.
summary,
5
CHAPTER 2
REVIEW OF LITERATURE
This
chapter
development
of
summarizes
consists
the
of six
sections.
The
theory of efficient markets.
first
The
previous research done on the subject of
section
efficient
futures
The
third section
models;
two
of these models will be chosen to use in
The
regressive
develops
fourth
reviews recent literature on
section briefly reviews the
integrated
moving
average
wheat
the
theory
modeling.
The
price
efficiency
behind
fifth
autosection
the efficiency tests that are to be undertaken in this
The
sixth
list
of
section considers data requirements and
the
second
markets.
tests.
traces
study.
availability.
references cited in this review is not complete.
The
However,
it
does contain those works considered by the author to be important to the
development and motivation of this project.
The Theory of Efficient Markets
Working
information
and
"necessary"
necessary
(1958)
and
writes
judgment,
and
"objectionable."
inaccuracies;
information.
that the sources of
classed
market
market
An efficient
mistakes
are
inaccuracies
as
market
contains
unexpected price changes are due only
Any error beyond that is objectionable
inaccuracy,
only
to
new
often
termed as speculative error, and likely results from the bad judgment of
traders
or
from
noncompetitive
market
situations.
Working
(1949)
6
implies
that,
if future price changes are
inaccuracies
must
objectionable
error is absent.
line
exist.
If
the
predictable,
changes
objectionable
unpredictable,
are
Samuelson (1965, p. 105) followed
of reasoning when he noted that "expected profits in an
market
can't
be increased by charts or any other
esoteric
this
efficient
device
of
magic or mathematics."
Fama (1970) took general statements such as the ones above, and, in
an article that has become a classic in the relevant literature, defined
concise
tests
for market efficiency.
First, Fama
(1970)
stated
the
there are
no
transaction costs involved in trading; (2) all available information
is
costlessly
on
following sufficient conditions for market efficiency:
(1)
available to all market participants; and (3) all
agree
the implications of current information for the current market price and
distributions
market
In such a market,
the
current
price would obviously "fully reflect" all available information.
However,
while
efficiency,
if
of future market prices.
the
above
conditions
they are not necessary.
"sufficient
numbers"
of
are
sufficient
The market may still be
investors
have
access
market
for
to
efficient
available
information, and there are no investors who can consistently make better
evaluations of available information than are implicit in market
CFama 1970).
one
Fama
prices
Next, Fama (1970) concisely defined an efficient market as
in which prices "fully reflect" all available
information.
Then
(1970) defined exactly what he meant by the term "fully ·reflect".
His theoretical development went as follows:
(1)
-
-
E ( p.J • t: + 1 lit ) = [ 1+ E ( r .J • t
where E is the expected value operator,
+1 :
It: ) l p.J t ,
P.Jt: is the price of security
j
7
at
time
t,
P.:t,t+l
intermediate
percentage
whatever
price
t+l
(With
reinvestment
cash income from the security), G,t+l is
return
(P.:t.t+l
-
It is
P.:~tliP.:~t•
a
the
general
at t, and the tildes indicate that Pt • .J+l and r.J,t+l
at
ECr.:~.t• 1 1ft>
t.
expectation
The
value
of
the
equilibrium
expected
notation of
return
return
theory
at
hand.
symbol
for
in
are
the
random
return
determined
The
is meant to imply, however,
(1)
any
one-period
expected
projected on the information It would be
particular
expected
of
set of information is assumed to be "fully reflected"
variables
the
is its price at
from
conditional
that
model is assumed to apply, the information
whatever
in
It
fully utilized in determining equilibrium expected returns. This is
sense
in which It is "fully reflected" in the information of the
is
the
price
P.:tt ·
Fama
(1970)
then
took
his equation
empirically testable implications.
assumptions
terms
of
(1)
and
developed
His development went as follows: The
that the conditions of market equilibrium can be stated
expected
some
returns and that equilibrium expected
returns
in
are
formed on the basis of (and thus "fully reflect") the information set It
have
a major empirical implication-- they rule out the possibility
trading
systems based only on the information in It that have
of
expected
profits or returns in excess of equilibrium expected profits or returns.
Thus let
(2)
X.:I •
t
+1
=p
.:I •
t +1
-
E( p.:I • t +1
lit )
Then
( 3)
-
E(X.:t,t+ 1
lit)
= 0
which, by definition, says that the sequence {x.:tt J is a "fair game" with
8
respect to the information sequence {It}. or, equivalently, let
(4)
z.J.t+1
= r.J.t+1
-
- E(r.J.t+1 :tt J
Then
ECz.J.t+ 1 :tt>
( 5)
so
that
the
= o,
sequence £z.Jtl is also a fair game with
respect
to
the
information sequence £1}.
In economic terms,
j at time t+l;
expected
x.J. t+l is the excess
it is the difference between the observed price and
the
value of the price that was projected at t on the basis of the
information It·
Similarly, z.J.t+l is the return at t+1 in excess of the
equilibrium expected return projected at t.
Let
a ( It > = Ca1 ( It >, ~ ( It: ) , ... , C4. ( It: >J
(6)
be
market value of security
any trading system based on It which tells the investor the
a.J(It>
amounts
of funds available at t that are to be invested in each of then
available securities.
The total excess market value at t+l that will be
generated by such a system is
n
vt+l
( 7)
=s
a.J Cit: Hr.J.t+l - ECr.J.t+l
a~ )Ji,
..:1-1
which, from the fair game property of (5) has expectation,
-
E(Vt:+l :tt:)
( 8)
The
testable
straightforward.
efficient
market
=
n
5 a..t Cit )E(z.J.t+ 1 :tt)
..:1-1
implications
of
Fama's
=0.
(1970)
work
are
quite
It is impossible to create a model that outpredicts an
to
the extent that expected profits
excess of "normal" profits or returns are generated.
or
returns
in
9
Fama
broke
(1970)
These
categories.
the
tests of
efficient
markets
categories were named weak form
test,
into
three
semi-strong
Fama's
judgment
efficiency,
requires
testing a market to see if price changes follow a random walk.
A random
form
test, and strong form test in order to
reflect
of how powerful each efficiency test was.
The
walk
first category,
implies
returns)
the weak form test for
that successive price changes (or
are independent and identically
successive
distributed.
one-period
Formally,
this
says
(9)
f(
which
is
the
t.
uf
that
an
the
conditional
independent
random
and
marginal
variable
are
In addition, the density function f must be the same for all
Expression
return
statement
distributions
probability
identical.
usual
r.J. t: ... 1 I It: ) = f ( r.J • t: +1 >,
model
(9), of course, says much more than the general expected
summarized by (1).
For example,
assuming that the expected return on securttiy
then we have
-
E(r.J.t:+ 1 11t:l
( 10)
= E(r.J.t:+
if we restrict
j
(1)
is constant over
by
time,
1 ).
This says that the mean of the distribution of r.J.t:+l is independent
of
·the information available at t, It:, whereas the random walk model of (9)
says in
This,
addition
however,
that
does
the entire distribution is independent
not preclude the possibility of a
trend
of
It:.
(random
walk with a drift) since expected price changes can be non-zero; earlier
work
by samuelson (1965) had previously shown that prices could
deterministic
trends while still fluctuating randomly.
careful to note that,
as shown above,
follow
Fama (1970) was
the fair game assumption is
not
10
sufficient to lead to a random walk.
i.e.
that
the
returns)
be
However,
game"
stationary
return
(zero
(indeed the
serial
entire
distribution
correlations)
through
while zero serial correlations are consistent with
model, the "fair game" model does not specifically
serial
correlations.
markets
that
However,
to
expected
The random walk implies much more,
In
his 1970 article, Fama
tested "fair game" efficient
did
were
"fair
require
zero
that
serially
many
correlated.
he felt that the small levels of serial correlation that
be often present in markets could not very likely be
profitable returns.
best
time.
the
show
to
regard
seem
exploited
Fama (1970) went on to explain that it is
the random walk model as a special case
of
for
probably
of
the
more
general expected return model ("fair game" model) in the sense of making
a more detailed specification of the economic environment.
basic
model
model,
with
conditions
time.
of market equilibrium is the "fair game"
a
random
arising
when
assumption
this
the
of
judged
relative
these
violations
environment.
viewpoint,
violations
of
the
random walk model are to be
Fama
themselves
pure
through
independence
But,
random walk
insights into the nature of
the
(1970) concluded his section on weak form
that there isn't much evidence against the "fair
return
environmental
expected.
to the benchmark provided by the
can provide
expected
additional
are such that one-period returns repeat
From
noting
walk
That is, the
when
model,
market
tests
by
game"
model's
form
tests,
with
whether
more ambitious offspring, the random walk.
Fama's
(1970)
contains
tests
current
prices
of
second
category,
the
semi-strong
efficient market that are
"fully
reflect"
all
concerned
obvious
publicly
available
11
information.
market
Each individual test is concerned with the
prices
to some kind of information generating
adjustment
event(s)
of
(e.g.,
export reports, domestic usage, dollar values, substitute prices, etc.).
Leuthold
and
Hartmann
comparisons
between
econometric
model
(1979)
interpreted
econometric
this
models and
test
futures
include
to
markets;
better utilizes available information
if
an
thereby
and
out-forecasts the futures market in question, then this is a valid semistrong
rejection
of
market efficiency.
When
semi-strong
tests
of
efficiency are carried out in this manner, the econometric models become
a norm with which to compare the futures markets.
(1970) third category,
Fama~s
of
efficient
"fully
reflect
its
whether
Fama
current
(1970, p. 415)
all
available information, is probably best
strictest sense) can be judged."
Tests
that
Osborne
(1966)
and
Scholes
(1969)
indicated
that
assumed
as
a
(interpreted
fall
into
would be concerned with above average returns being
by such factors as monopolistic access to information.
noted
viewed
against which deviations from market efficiency
category
prices
strong efficient markets model, in which prices are
benchmark
in
markets that are concerned with
reflect" all available information.
that, "The
to
the strong form test, contains tests
this
generated
Niederhoffer and
such
market
inefficiencies do occur by showing that above average returns are earned
by New York Stock Exchange specialists and corporate officers.
Since
Fama (1970), there have been many articles dealing with
the
concept of efficiency and the characteristics of efficient markets.
The
conventional
author,
so
Fama
(1970)
approach to efficiency was
taken
little discussion will be made of later approaches.
by
this
It
is
12
pertinent to note, however, that later works do indicate that there
be
some problems with Fama's (1970) definition of efficiency
may
since
no
account is taken of the costs of acquiring information and/or changes in
the
variability of the price series (Grossman and Stiglitz,
fact,
Grossman
efficiency
to
and Stiglitz (1980) showed that, for
hold,
costless information is
condition, but also a necessary condition.
particular
not
the
only
In
property
of
a
sufficient
This implies that, even if a
model's forecast is more accurate than the forecasts of
futures market, inefficiency does not necessarily follow.
to
1980).
For a
the
market
be inefficient, it is necessary to have a model that forecasts
accurately
than the market; however, this is not sufficient for
inefficiency.
To
be
sufficient for
market
inefficiency,
more
market
the
risk
adjusted returns must be large enough to cover all modeling costs.
Efficient Futures Market Research
Both
the efficient market model and the special random walk
model
discussed in the previous section imply that no mechanical trading rules
can be used to increase profits.
Fama's
(1970)
A large body of research that followed
article attempted to reject efficiency
by
constructing
successful
trading rules or by testing for serial correlations with the
idea
serial correlations indicate the possibility
that
trading
study,
rules.
the
of
profitable
Since this will largely be the approach taken in
articles
discussed
in
the
following
section will
this
be
congregated around these ideas. Other approaches to efficiency tests
of
futures
of
markets do exist and will be briefly summarized at the
this section.
end
13
cargill
464
and Rausser (1975, p. 1049) weak form
futures
contracts from seven commodities
efficiency
(corn,
oats,
copper, live beef cattle, and pork bellies) and
soybeans,
obtained
weak-
rejections of efficiency for the set of results as a whole:
"the
wheat,
form
tested
results
of this analysis clearly indicate that there are a
significant
number of departures from randomness. Thus the random walk model must be
rejected."
They did note in their paper that this was a rejection of
random
walk
and therefore did not necessarily imply that
tested
were
inefficient.
paper,
they
applied a g-percent filter (a quite popular
that
In fact, in an interesting
the
aside
markets
in
their
trading
rule
gives buy-sell signals based upon percentage changes in price)
computer
produced
generating
random
series of market
substantial profits.
prices
and
felt
this
was strong evidence in support of the contentions that the
walk
model
markets
was
not an accurate
explanation
of
efficient
in
that
random
commodity
that positive profits from the g-percent filter
and
to
succeeded
Cargill and Rausser (1975)
a
were
not
necessarily indications of serial correlation as previously believed.
Leuthold and Hartmann (1979) performed a semi-strong form test
efficiency
on
constructing
which
Chicago
Board of Trade's
hog
futures
and
market
an econometric forecasting model to serve as a
to compare the Chicago Board of Trade's hog futures
econometric
data
the
norm
(1979, p. 484) stated that, "By design, the econometric
is
simple
kept
inefficient,
because,
further
if a simple model shows
elaboration
becomes
the
unnecessary
The
monthly
Leuthold
Hartmann
market
to
by
with
market.
model was a two equation demand-supply model using
closely following the well known cobweb model.
for
test
and
model
to
be
the
14
efficient
market
Hartmann
(1979)
hypothesis."
were
able
On the basis of
to
reject
RMSE,
(semi-strong
form
test)
efficiency
hypothesis.
comparison
because of the importance of weighting large errors
They
chose to use RMSE as
and
Leuthold
the
the
statistic
of
greater
than small errors in a forecasting model.
Rausser
efficiency
Carter
and
on
the
(1983)
Chicago
performed
Board of
a
semi-strong
Trade's
soybean
test
complex.
of
They
followed fairly closely the framework set forth by Leuthold and Hartmann
(1979)
by
compare
building
the
rejection
was
an econometric forecasting
futures market and succeeded in
of market efficiency.
model
with
obtaining
a
to
semi-strong
However, they did not feel
that
this
in fact a true rejection of efficiency; rather, they felt that
necessary
condition
for
sufficient
condition
for efficiency rejection would require
cost
of
constructing
incremental
appropriately
benefits
Rausser
efficiency
rejection
and utilizing their model
cost/benefit condition).
in
which
adjusted
had
been
did
not
by
risk
met.
the
The
that
the
exceed
the
(relative
Bias was also added as a comparison
statistic
and Carter's (1983) analysis because they felt that
for
a
model to meet the necessary condition for efficiency rejection it had to
do
this
so
in both terms of volatility (RMSE) and bias.
concept
of
meeting both a bias and a
They
volatility
referred
to
constraint
as
I -"relative
accuracy."
In concluding their article, Rausser
and
Carter
(1983, p. 477) pointed out that, while only the necessary condition
for
efficiency rejection had been quantitatively met by their research, they
had
deliberately kept the predictive models simple, thereby
the
marginal
cost
of use and giving a
high
probability
minimizing
of
meeting
15
sufficiency
requirements
opportunities
returns
exist
whicn
indicate
"It
in the soybean complex for excess
exceed
that,
for efficiency rejection:
normal
returns adjusted
appears
returns,
for· risk."
in later research, they planned to
that
do
i.e.,
They
market
did
trading
simulations with their model to test if actual excess returns do
exist.
A simple
market
trading
rule
using their model as an
indicator
of
direction was to be used in developing a trading strategy.
Kamara
(1984) summarized other research that had occurred
futures market efficiency area over the last twenty years.
the
results
researchers
different
general
were
fairly
the
same
or
conclusions.
consensus
that
as
a
the
similar
As a
since
questions
who
in
reached
(1970)
the
the
large
large
enough
that reports on market position and intent had to
Commodity Futures Trading Commission), could
whole,
ability
especially
traded
the
different
often
forecasting
speculator,
speculator
better than the futures market.
Fama
disconcerting
In the area of price
was
(defined
quantities
the
found
asking
speculator
with
he
in
be
filed
forecast
pri.ce
This result would be consistent with
semi-strong efficiency rejection.
However, it
should
a
be
noted that the majority of the studies reviewed by Kamara (1984) did not
take
into account the cost of the speculator's forecasting
information
or the possibility that the speculators were being rewarded for
risk.
for
Therefore, these results represent only the necessary
efficiency
rejection
and do not
meet
sufficiency
bearing
condition
requirements.
Also, it should be noted that Hartzmark, in a 1987 study based upon
the
Commodity Futures Trading Commission's confidential files, was unable to
16
find
any
evidence
to support the contention
that
speculators
walk
efficiency
could
forecast price.
As
for
the
special
case of the random
tests,
most
of the research on random walk models of the futures markets
was
summarized
by
Karama
(1984)
found
some
evidence
correlation, especially short run serial correlation.
is
consistent
again
the
nonrandom
with a Fama (1970) weak form
components
efficiency
unless
is
some
not sufficient
serial
While this result
rejection
results aren't very compelling.
of
that
of
efficiency,
The mere existence of
evidence
unexploited opportunities
some
to
reject
general
for
above
average
profits are created by this Jack of randomness in price.
A 1980
argument by Grossman and Stiglitz probably best summarizes
the current thoughts on futures market efficiency.
futures prices
reflected all available information, then traders
no incentive to gather information.
have
obtain,
then,
in
equilibrium,
held
by
information
earn
a higher return.
no
informed
prices
information
market
They argued that
If information is
traders,
so
that
those
would
costly
will reveal only part
who
Costly information will
if
of
to
the
acquire
result
in
prices that do not reflect all available information even though
traders
behave
suboptimally.
This
again
emphasizes
current
theoretical trends towards redefining Fama's (1970) efficiency rejection
tests
as
tests
for
only
the
necessary
conditions
for
efficiency
rejection and not tests that satisfy general market efficiency rejection
criterion.
To
meet
rejection,
the
both necessary and sufficient
potential
criterion
expected returns from
for
efficiency
exploitation
of
the
17
perceived failings in the market price must be greater than the cost and
risk of gathering and utilizing the necessary information.
Wheat Price Forecasting Models
This
section
forecasting
read
or
reviews some of the recent models that are used
wheat prices.
easily
available publications
This
1i terature.
Only models that were published in
were
considered
was done to insure that the cost
of
for
commonly
as
relevant
acquiring
and
using these models was minimal.
Westcott
et
al. (1984) and Westcott and Hull (1985)
built
wheat
price forecasting models for the United States Department of Agriculture
(the
USDA is the largest publisher of agricultural commodity and
forecasts).
hyperbolic
price,
The
model
function,
(P-a)(S-d)
= c,
was
based
where P is
on
the
the
general
quarterly
wheat
cs- 1
year,
a
Solving the above equation for price gives
To represent the different effects of
separate
important
usage,
•
c parameter was assumed for
in the wheat industry.
market
filled.
reflect
each
Westcott et al.
since the wheat market had grown sharply
develop
stocks
this "relative usage" measurement
required
(1984)
"stickiness" of
the
is
amount
of
felt
that,
over time, it was necessary to
of stocks because
a greater level of stocks to keep
term
=
It
quarter.
quarterly
a
marketing
Lagged price was also included as an independent
short
P
through
to note that stocks, s, were measured relative to
u,
are
To avoid nonlinearities in estimation, the parameter d was
assumed to equal zero.
+
developed
s denotes quarterly ending stocks of wheat, and a, c, and d
parameters.
a
they
price
wheat
larger
channels
variable
prices.
to
Price
18
was
"stickiness~
thought
to reflect
partial
adjustments
caused
by
relative bargaining positions of market participants and/or expectations
based
upon
complete
incomplete
market
information,
which
thereby
price adjustments in the short run. The preceding
prevented
adjustment
resulted in the following general equation:
(i
4
P =a+ b lag(PJ + s c,D, (5/U)- 1
i=l
1)
•
o, are quarterly dummy variables (equal to 1 in the i-th quarter,
Where
0, elsewhere), lag(PJ is the one quarter lag of price (P), and a, b, and
c,,
i=1, ... ,4,
denote
are
quarters,
April-May
quarter,
October-December
c:~.D:~.
(5/U)- 1
hyperbolic
estimated.
smaller as
"i"
the
i=3 is the June-September quarter, and i=4
is
the
Westcott
et
(1984)
al.
included
to allow a different effect of stocks on
the
prices
as
the
For any
given
5°/UO, the resulting prices would be
time from harvest increases.
This is
from one hyperbolic curve to the next.
stock-to-
stock-to-use
expected
to
indicated
The actual
by
model
estimated from 1971-81 (44 observations).
The final empirical results were:
(12)
P = 0.041 + .830 lag(P) + 1.071 01 (5/U)- 1 + .389 02 {5/U)- 1 +
(0.2)
(12.7)
(1.9)
(0.9)
2.385 03 (5/U)- 1 + 2.401 04 (5/U)- 1
(2.6)
R2
in
Thus, equation (11) is expected to yield a family of four
curves that represent price's relationship to the
such
movement
subscripts
is
use ratio for each quarter (see Figure 1).
ratio,
The
where 1=1 is the January-March quarter, i=2
quarter.
terms
each quarter.
parameters to be
= .875
•
(3.1)
MAE <mean absolute error) = .270
be
a
was
19
PRICE (p)
P01 '
,
,I
\
}
..
P~ --t'--\\-~"..
r•
Po3
pO
4
S~U
0
STOCKS-TO-USE RATIO
h = harvest quarter
h + 1 a 1 quarter after harvest
h + 2 • 2 quarters after harvest
h + 3 a 3 quarters after harvest
P = prtce per bushel of wheat
~ • harvest quarter prtce tor a gtven
~., • harvest + 1 quarter prtce tor a
~. 2 • harvest + 2 quarter price tor a
~. 2 • harvest + 3 quarter prtce tor a
SO/UO • a gtven stock-to-use ratto
(S/U)
stock-to-use ratio
gtven stock-to-use
gtven stock-to-use
gtven stock-to-use
(5°/UO)
ratio (5°/UO)
ratio (5°/UO)
ratto (5°/UO)
Ftgure 1. Relattonshtp Between Quarterly Prtce and Stocks-to-use Ratto
20
The
sign
of the coefficients on the stock-to-use ratios were
and
tended
positive
to diminish as the time from harvest increased.
This
met
with the expectations of Westcott et al. (1984).
To
al.
assess the predictive capabilities of their model, Westcott
(1984) forecasted quarterly price for the years 1982 and 1983.
1982
a mean absolute error (MAE) of 24.2 cents per bushel was
et
For
obtained
and for 1983 an MAE of 31.1 cents per bushel was obtained. This was felt
to be acceptable performance for a wheat forecasting model although they
noted
that some problems with forecasting may have been caused
by
the
1983 PIK program and the 1983 drought.
Another
is
the
publicly available source of commodity forecasting
many
books
and pamphlets published
analysts. Schwager (1984)
contributed
by
futures
models
traders
and
to this body of information when
he published the book A Complete Guide to the Futures Markets. While not
explicitly
presented
creating
and testing a wheat
forecasting
model,
theoretical arguments for a general model form.
Schwager
Since
this
book represented a fairly new and available publication on wheat
market
models, it was chosen as a literature source that met the general
cost-
availability framework
discussed earlier.
The following
section
will
develop Schwager's (1984) general wheat model.
The basic model proposed by Schwager is:
(13)
Where
DP
DP
question,
=a
+ b(D5/ES).
is the average deflated cash wheat price for
a
and b are parameters to be estimated
by
the
period
regression,
in
and
05/ES is a ratio of five period average disappearance of grain stocks to
ending
grain
stocks.
The five period moving average
of
grain
stock
21
disappearance, 05, was used to normalize stocks since Schwager felt that
this
would be a more representative measure of the size of the
market.
A single period, D, could make the model unstable by making it prone
being
affected
It
market.
was
on
average
by
short period abnormalities that can
suggested, however, that the
stock disappearance be
occur
length
of
varied until "best
in
the
model
to
any
moving
fit"
is
obtained.
Schwager viewed the general model (13) as a logical starting
for
constructing price forecasting models of the grain
this
basic model was
were
ratios
Two potential right-hand
suggested are: (appropriately
and
impressive
trade
dollar
model fits
Once
tested, the analyst can then experiment with
addition. of other variables.
that
markets.
point
(~
values.
lagged)
Schwager
side
variables
wheat-to-corn
stated
that
the
some
of .89 to .98) had been obtained using
price
very
these
methods, but did not explicitly show the actual models.
There
are
models
in
followed
the
general framework of Schwager (1984) and/or Westcott et al. (1984).
All
models
and
publications.
many
other
wheat
price
However,
those
reviewed by
forecasting
this
author
had lagged wheat price or wheat-to-feed grain price ratios
either lagged or forecasted supply-disappearance variables on the righthand
side.
Therefore, the two wheat price models discussed
above
are
felt by this author to be representative of the literature available.
General Auto-regressive Integrated Moving
Average Modeling Theory
Box
form
of
and Jenkins (1976) are generally considered the creators of
time series analysis that is referred
to
as
a
autoregressive
22
integrated
defined
CAR)
moving
average
as follows:
lag,
the
differenced,
d
and
the p represents the order of
represents
the
the
number
of
of
analysis
emphasis
Cp,d,q)
autoregressive
the
the
is
data
moving
were
average
(The Cp,d,q) will not be presented unless a
In this approach to time
specific model structure is being discussed.)
series
the
times
q represents the order
(abreviated MAl error term.
The
{ARIMACp,d,Q)) modeling.
the goal is generally
is placed on explanation.
prediction;
therefore,
little
As a result, ARIMA modeling
has
a
much more limited application than most forms of time series econometric
modeling; econometric models are often as concerned with explanation
as
with prediction.
ARIMA modeling is generally broken down into a four-fold
exercise.
The
four basic exercises are:
timation,
(3)
diagnostic checking, and
three
steps
satisfactory
this
are
iterative.
The
(1) identification,
(4)
fourth
forecasting.
step
is
taken
results are obtained from steps 1 through 3. The
section will discuss the characteristics that a data
exhibit
iterative
first
only
when
rest
to be a candidate for ARIMA modeling, and will present a
an
in-depth discussion refer to
Time
Series
of
need
brief
Brevity was
considered reasonable since ARIMA modeling is a well known and
For
es-
The
series
discussion of each of the steps involved in ARIMA modeling.
process.
(2)
accepted
Analysis:
Forecasting and Control (Box and Jenkins, 1976).
data
Candidate
characteristics.
contain
intervals
data
(Box
processes for ARIMA models must
These
that
and
was
characteristics
measured
in
are:
equally
(1)
have
the data
spaced,
Jenkins (1976) suggest at least 50
some
basic
set
must
discrete
time
observations),
23
(2) the mean of the data series must be constant through time,
. variance
(3)
the
of the data series must be constant through time, and (4)
the
autocorrelation function must be constant through time;
must
be
autocorrelation
a function of lag length only, i.e. relative position
in
the
series cannot have any effect on autocorrelation.
candidate
a
If
data
set
satisfies
preceding
the
all
characteristics, then it is referred to as second order stationary (505)
and
is
data
a good candidate for univariate, Box and Jenkins ARIMA.
set
does
methodology
series
is
that
not satisfy these characteristics,
then
to difference the series to try to obtain
cannot
meet 50S criterion is not a
It
a
the
accepted
sos.
A data
candidate
for
ARIMA
modeling.
If a data set meets the requirements tor ARIMA modeling,
step
is the identification stage.
the
Identification is the step in which
one or more possible ARIMA models are chosen as candidates for
the
forecasting
correlations
devices
estimated
model.
between
next
Two graphical devices
are
used
observations within a single data
to
The
measure
series.
are called an estimated autocorrelation function (act)
partial autocorrelation function Cpacf).
building
These
and
an
estimated
act
and pact measure the statistical relationships within a data series
and
are helpful in giving a feel for the patterns available in the data.
I
The estimated act and pact are then used as guides in choosing
I
'
or
that
it.
more
ARIMA models that seem appropriate.
Thus, the basic
every ARIMA model has a theoretical act and pact
idea
associated
At this stage the theoretical acts and pacts are compared with
estimated
acts and pacts in order to select a model
whose
one
is
with
the
theoretical
24
acfs
and
pacfs most closely match the estimated acfs and
pacts.
The
data is not approached with a preconceived idea about what model to use,
as
in the case of econometric models; rather, the data is
expected
to
"talk" through the estimated acfs and pacfs and ihereby reveal the model
of
choice.
stage;
it
Models are only chosen tentatively
at
the
identification
a tentative model will not be accepted as a final
proves
adequate in the estimation and diagnostic
Otherwise the identification stage must be
model
unless
checking
stages.
rep~ated.
The estimation stage is where precise estimates of the coefficients
of
the chosen
signals about
model are obtained.
This stage
the adequacy of a model.
In
provides
particular,
some
the
warning
estimated
coefficients must meet certain mathematical constraints (size and
or the
tentative model is rejected.
constraints
will
requirements.
For
not
satisfy
doesn't
A model that
stationarity
and/or
a more detailed explanation of
meet
sign)
these
invertibility
stationarity
and/or
invertibility see Pankratz (1983).
The third stage of ARIMA modeling is the diagnostic checking stage.
Box
and
determine
Jenkins
(1976)
suggested
some
diagnostic
checks
if an estimated model is statistically adequate.
This
is mainly concerned with looking at the residuals in order to
if
only white noise remains.
If a model is shown to be
to
help
stage
determine
inadequate
in
this stage, then stage 1 (identification) must be returned to.
The
Assuming
fourth
and
final
step in
ARJMA
modeling
is
that all the requirements of steps 1 through 3 are
the model is then used to derive forecasts.
If the
forecasting.
satisfied,
ARIMA model
is indeed the correct one, then forecasts made with this model are
chosen
said
25
to
be
optimal.
smaller
This means that no other univariate
forecasts
have
a
mean-squared forecast error CMSE).
Development of an Efficiency Test
for the Wheat Futures Market
The following section traces the general ideas and concepts
the efficiency test that is undertaken by this study.
efficiency
in
this
section
refer to the Fama
behind
All references to
(1970)
definition
of
efficiency.
The
market
that
is tested for efficiency in this
Chicago Board of Trade's wheat futures market.
the Chicago Board of Trade's
study
is
the
The contract tendered on
wheat futures market is for number 2 soft
red winter wheat deliverable upon contract expiration to any of
several
designated
is
subject
cash
delivery
to
price
points.
One such point of delivery that
location premiums or discounts is Chicago,
for
number 2 soft red winter wheat at
thereby
Chicago
not
making
a
logical
choice for a data series to be used in this study.
The
next step is to choose a time interval to forecast
Chicago
Board
forward
price predictions of any length less than 15
close
of
Trade's wheat futures market is
(contract
(contracts
traded)
predictions)
five
given
capable
length)
and
the
number· of
indicates that near term
"
the
making
However,
the
price
predictions
made
contracts
experience the greatest trading volume.
of
months.
examination of the relationship between the length of
prediction
since
(short
Since
contracts (December, March, May, July, and September)
length
there
are
traded
per
year, each contract spends approximately two and one-half
months
26
being the near term contract.
number
2
The closest any readily available,
soft red winter wheat data set could come
prediction
interval
was in quarterly format.
As a
to
cash,
matching
result,
this
quarterly
intervals were chosen to be the standard by which efficiency tests
made;
quarterly,
a
series
cash price, number 2 soft red
winter
were
wheat
was obtained for the period from the first quarter 1966
data
to
the
2nd quarter 1986.
After
step
selection of the prediction interval and data set,
becomes
efficiency
selection
tests
proposed . by
of
used
in
in
1970.
Fama
the
appropriate
this study
closely
efficiency
follow
The version of the Fama (1970) efficiency test that
requires
compare
test.
framework
is
undertaken
price prediction capabilities of the market
Conclusions on market efficiency
efficiency
reached.
relative
to
The
the
the creation or selection of a standard (norm) with
the
the next
in
which
to
question.
or, at least, conclusions about market
the model chosen for comparison, can
Logically, "simple" (easily constructed and
then
utilized)
be
models
should be chosen first since an efficiency rejection by a "simple" model
precludes the necessity of creating a more complex model.
It must
also
be recognized that a Fama (1970) form rejection of efficiency represents
only
the
Therefore,
necessary
since
the
condition
for
general
sufficient condition
efficiency
for
efficiency
rejection.
rejection
requires that model cost be taken into account, the cost of creating and
utilizing complex models often makes them fail sufficiency criterion.
Perhaps
random walk;
the
most simple model of a market proposed is that
of
a
it takes minimal knowledge and time to test the hypothesis
27
that
a
data set is a random walk.
random
walk,
model
or
then
follow
If the data set does not
follow
a
build
a
this indicates that it may be possible to
some
other
trading
rule
that
predictions than those generated by the market.
will
allow
better
The general cash
wheat
random walk model is:
WPt:
(14)
Where
=a
+
13WPt:-t ·
WPt:-t represents cash, number 2,
Chicago
in
the
(t-i)th quarter,
soft red winter wheat price
a is an intercept
parameter
to
at
be
estimated, and 13 is a slope parameter to be estimated.
The
number
random walk model has 13 equal to one and a equal
best
to
whatever
represents the market drift, i.e. a market with
no
drift
would have a equal to zero, whereas a market with positive growth
would
have
a
greater than zero.
that
13
= 1.
freedom
(n
hypothesis
Therefore, the hypothesis to be
The T test is the appropriate test with
is
the
that
13
number
=
0
of
is a
observations).
Fama
(1970)
n-2
tested
is
degrees
of
A rejection
weak
form
of
the
rejection
of
efficiency.
If
the wheat price series do not follow a random walk,
then
this
indicates the possibility of building an ARIMA model to compete with the
wheat
futures
market.
A random
walk
model
is
an
AR(l)
process;
therefore, the rejection of a random walk model poses the possibility of
creating
a model that has an AR(p) process with p>l.
An
model
where the exact form is not ARIMA(l,O,O) indicates
price
does not "fully reflect" available information.
succeeds
ARIMA(p,d,q)
that
current
If such a
model
in rejecting wheat futures market efficiency, then this
would
represent a Fama (1970) semi-strong rejection of market efficiency.
28
Models
other
than
ARIMA
can be used to
serve
as
a
norm
for
efficiency comparisons; any model or rule that allows for either
actual
price
viable
prediction
candidate for
an
or
predicts direction of price change
efficiency test.
Two
other
is
competing
a
models
were
selected from the literature to serve as comparison norms in this study.
The
general form of and theory behind the models selected
and
model (13)) are given in a previous section.
chosen
over
model
creation
currently in the literature.
to allow for tests
Model
of
(model
selection
models
the largest, most easily available source of
predictions.
is
that
are
This is especially relevant in the case of
model (11) since this model is one that the USDA advocates.
possibly
(11)
The USDA is
commodity
price
Another benefit of model selection over model creation
is
that with model selection the right-hand side variables don't have to be
derived and defended.
The
the
statistics that will be used for comparison between models
wheat
market and the wheat futures market are RMSE and
selected statistic of comparison is RMSE since it effectively
large
prediction
important
could
also
of
will
This
prediction
more effectively lead to resource allocation problems.
as a statistic of comparison to effectively rate
resource allocation.
consistently
A biased model or
misallocate resources through
time~
futures
Both
RMSE are commonly accepted measures tor tests such as these.
is
that
Bias
is
how
the
futures market fared against the other chosen models in the
consistent
The
penalizes
errors.
since it is the large errors in wheat price
chosen
wheat
errors more than small prediction
bias.
of
area
market
bias
and
29
The final empirical step taken in this study only occurred
because
one of the preceding models (ARIMA) succeeded in obtaining a Fama (19701
semi-strong
efficiency
rejection of market efficiency. Since a Fama
meets
only
the
necessary
condition
for
rejection
general
efficiency rejection, the sufficient condition for efficiency
must
be
examined.
rejection
enough
of
In order to meet sufficiency
returns
(risk
adjusted)
utilizing the competing model.
to cover the
Returns from
market
rejection
requirements
market efficiency, a competing model must
cost
for
a
high
generate
of
of
building
and
trading the model that met
the necessary criterion will be measured, the cost of building the model
will
be
estimated, and the opportunity cost of money invested
model will be figured at a 101 discount rate.
in
the
However, the returns from
speculating with a price predictive model need to be adjusted for
risk
before
risk
comparing
them to returns from other
investments.
Since
adjustment is a function of personal preference, no attempt will be made
to
adjust
have
to
returns for risk.
choose
Individuals that review this
a method of adjusting returns to
reflect
study
will
their
risk
preferences and thereby reach a conclusion as to whether the
sufficient
condition for wheat market efficiency rejection is met.
Data Availability and Requirements
!
Quarterly
were
measures
of the following variables from 1966
required: number 2 Chicago cash price for soft red
producer
trade
readily
price
index (PPI}, total grain usage,
ending
weighted dollar values, and cash corn prices.
available
from the following
government
to
1986
winter
wheat,
grain
stocks,
All the data
publications:
were
Wheat
30
Outlook
and
Situation
Report,
Feed
Outlook
and
Situation
Report,
Agricultural Outlook, and The Economic Report of The President.
Efficiency
tests require that an accounting of the costs
of
data
gathering be kept in mind; however. the data required for this study did
not
represent a problem in this area.
obtained
All the data sources are
from libraries or can be ordered on an annual basis
that total less that $100.
for
easily
fees
31
CHAPTER 3
EMPIRICAL RESULTS
The
study.
previous
This
estimation
chapters
chapter
of
the
presented the theoretical basis
summarizes
the
actual
empirical
models used in this study is
for
this
results.
completed
The
using
the
statistical package DYNREG (Burt et al., 1986).
chapter
first
~ection
the results of fitting ARIMA models to the cash wheat
market.
This
presents
The
with
is
divided into five sections.
second section gives the results obtained from
model
efficiency
(11).
The third section gives the
testing with model (15).
The
efficiency
testing
results
obtained
from
The fourth section
provides
the
from modeling the producer price
index.
The
results
acquired
section
presents the costs of utilizing and the potential returns
fifth
from
speculating with the best competing model.
Soft Red Winter Wheat ARIMA Models
Random Walk Model Results
An
ARIMA modeling process begins with a visual examination of
the
candidate data series to check for obvious problems that the series
may
exhibit
regarding
the
nominal
and
real cash wheat series raises some real
whether
the
series has constant mean and/or constant
nominal
data series appears to exhibit a slight growth rate,
50S; visual examination (see Figure 2) of
both
questions
variance.
and
as
to
The
both
11
10
9
+
•
B
0
0
NOMINAL WHEAT PRICE
REAL WHEAT PRICE <1985•100>
7
L 8
L
A
R
s
w
N
5
4
3
:J
~~~i~l~i~i~IMi~i~lrrtrjTITiTITITiTITITITI~j~l~i~l~i,l,l,i~l~i~jrriTITITITITITITITI,j~i~i~l~iMI~IrriTITITjTITITITITITITI~ITITjTITI~I,i,i,l~i~i~i~J~i~lrrtriTITITiTITITjTITITITI~iTITI~i~l~j
0
10
20
30
40
50
60
70
QUARTERS C1966COTR1>-1986COTR2>l
Figure 2.
Nominal and Real Cash Soft Red Winter Wheat
eo
90
33
the
nominal
variance
and
real data series appear to
changes
quarter
exhibit
in the quarters of 1973-1974
some
structural
(specifically
of 1973 and the first two quarters of 1974}.
the
4th
At this point
it
became necessary to choose to work with either the nominal or real price
series.
Since
the
futures market's price predictions are
nominal
basis, the nominal data series were chosen as
series to work with to create the ARIMA model.
then
on
a
appropriate
The nominal series
were
split in half (41 quarters per half} in order to compare the
mean
and variance of the two halves.
set
the
made
equals
equals
The mean of the first half of the
$2.39, whereas the mean of the second half
$3.41.
of
the
data
series
The variance of the first half of the data set is
equal
to $1.64 whereas the variance of the second half the the data set equals
$0.35. '
The
and
mean and variance statistics indicate a problem with 505.
Jenkins (1976) suggest differencing to deal with problems
nature,
so
this
series
became
caused
by
is initially the approach
constant mean; however, the
the
taken.
constant
1973-1974 quarters did not improve.
The
of
this
differenced
variance
In
Box
fact,
problem
as
the
degree of differencing increased, the constant variance problem actually
worsened.
At this point either a time series approach other than
ARIMA
or a dummying of the problem quarters in 1973 and 1974 became necessary.
I"
Visual
examination
through
1974
of
a quarterly price chart
1988 indicates that
frame
wheat
large variance appearing in
(352
1900
the
1973series.
Historically, there exists an explanation for the violent price
changes
this period.
is an anomaly in this longer
from
quarter)
of
time
~he
for
In 1972 the Commodity Credit Corporation (CCC},
eager
34
to
unload
grain stocks in government storage, struck
a
bargain
with
drought stricken Russia which completely emptied the CCC stocks of grain
(400
million
Organization
bushels)
of
1974.
Also,
in
Petroleum Exporting Countries
thereby
bringing
factors
contributed
experienced
by
an
this
time
(OPEC)
cheap
strongly
tremendous
in this time period.
the
the
embargoed
oi I,
Both
these
energy.
end to the era of
to
frame,
price
However, it can be inferred from
1900-1988 quarterly wheat chart (indicating the 1973-1974
an
variance
the
time frame as
anomaly) that both the OPEC oil embargo and the Russian
wheat
deal
Given, then, that the price variance of the fourth quarter of
1973
were uncommon occurrences and unlikely to reoccur.
and
of
the first and second quarters of
abnormality,
it
seems
approach to stationarity.
1974 can be described
reasonable and prudent
to
take
the
as
dummying
A zero/one dummy is regressed as a right-hand
side variable where the fourth quarter of 1973 and the first and
quarter of 1974 are dummied out.
difference
timing
out
equation
of
the
an
The dummy variable is included in
(distributed lag effects) to allow for
1973-1974
second
variance
effects
since
the
a
gradual
this
better
represents the gradual disappearance of the real world market influences
occurring during this time frame.
I
compensate
making
for
The zero/one dummy should effectively
the variance problems of the 1973-1974
period, thereby
an ARIMA representation of this data series possible (OYNREG,
a
nonlinear least squares algorithm for distributed lag models, is capable
of
dealing
1986).
with
the slight drift in the data
series
<Burt
et
al.,
35
Because seasonality exists in the quarterly wheat data series,
other
modification
is made in the basic ARIMA process.
The
approach
taken to this problem is to dummy out the seasonal component.
quite
straightforward
(Johnston, 1984).
fourth
carrying
any
This is a
and well accepted procedure for seasonal
models
Zero/one dummies are used for the second, third,
quarter of each year which results in the intercept
seasonality
information that is
present
one
and
coefficient
in
the
first
quarter.
The first ARIMA(p,d,q,J model to be considered is the
model (random walk model).
Tests of whether markets follow random
models are Fama (1970) weak form efficiency tests.
the
general
ARIMA(l,O,O)
Model (14) presented
form (ARIMA(1,0,0J) of a wheat market random
walk
The sos requirements resulted in the general form having to be
slightly
to
deal
with
the seasonality
and
walk
variance
model.
modified
problems
problems) of our particular data set, i.e. seasonal dummies and a
for
the fourth quarter of 1973 through the first two quarters
The result of these
were added as previously discussed.
on
(505
dummy
of
1974
modifications
the general random walk model is:
(15)
PWt.
=a+ /i 1 02 + /i2 03 + /i3 04 +
/i4 073 + cx:PWt._ 1 + Ut..
with
Where
ut.
PWt.-~
= Et..
is the cash price of number 2 soft red winter wheat in
(t-i)th quarter, 02-04 are the seasonal dummy variables for the
third,
variable
and
fourth quarters of the year respectively, 073
for the fourth quarter 1973 through second quarter
period, and Ut. is the error structure <MA(O)J.
is
the
second,
a
dummy
1974
time
36
To
be
a random walk with a drift, the coefficient
on
the
PWt_ 1
term, oc, has to be equal to one (the other coefficients will pick up the
drift effects); the null hypothesis tested is
alternative
is
the
hypothesis
T test
with
that~
that~
is not equal to 1.
n-6 degrees of
freedom
equals 1 versus the
The appropriate
(n
is
the
test
number
of
observations).
The empirical results of estimating model (15) are:
(16)
= .37572
PWt
(2.98)
- .18374 02 - .0010047 03 + .097382 04 +
(2.26)
(1.07)
(1.21)
1.1155 073 + .8638 PWt-1 + Ut.
(4.65)
(21.35)
with
ut = Et.
lf2
The
null
= .88.
hypothesis that model (16) represents a random
tested at the 1 percent level of confidence.
walk
is
The calculated T-statistic
to test the significance of the estimated parameter of the lagged
price
of wheat CPW> regressor is:
Tc.a1.7b)
At
the
1
= 3.36.
percent level of significance the hypothesis that
the
cash
wheat market follows a random walk is rejected.
The rejection of the ARIMAC1,0,0) model (random walk with a
of
the
cash
wheat
market
introduces
the
ARIMA{p,d,q) forms better modeling this market.
this
section on random walk models,
"simple"
possibility
of
drift)
other
However, before leaving
it is pertinent that the so-called
random walk model be discussed since the "simple" random
model of futures markets is quite popular in the efficiency
walk
literature.
37
The general model that represents the "simple" random walk is:
PWt:
( 17)
= adj ( PWt:-t )
+ Ut:.
Where PWt-t is wheat price in the (t-i)th quarter, and the (adj)
prefix
represents adjustments made for predicted inflation.
Model
(17)
adjustments,
discussed
the
PPI
is used to forward predict wheat price (the
(adj), are acquired
by using the ARIMA(l,O,O)
inflation
PPI
model
in a following section to obtain one step ahead forecasts
which are then used to adjust price).
Table
1
presents
of
the
results of the forward price predictions of the simple random walk model
(from first quarter 1982 through second quarter 1986) and the calculated
RMSE and bias statistics.
Table 1.
Price Predictions with a Random Walk Model
Time Period
I
1982
1982
1982
1982
1983
1983
1983
1983
1984
1984
1984
1984
1985
1985
1985
1985
1986
1986
I
II
I II
IV
I
II
II I
IV
I
II
II I
IV
I
II
II I
IV
I
II
Cash Price
Prediction
Residual
3.59
3.31
3.18
3.23
3.36
3.53
3.62
3.55
3.57
3.51
3.47
3.49
3.58
3.27
2.83
3.46
3.40
2.52
3.70
3.54
3.35
3.12
3.14
3.34
3.54
3.72
3.64
3.79
3.65
3.57
3.58
3.60
3.22
2.70
3.45
3.32
0.11
0.23
0.17
-0.11
-0.22
-0.19
-0.08
0.17
0.07
0.28
0.18
0.08
-0.00
0.33
0.39
-0.76
0.05
0.80
RMSE
Bias
= .3193952
= 8.220535E-02
38
When
Trade's
compared to predictions made by the actual Chicago
wheat
predictions
futures
don't
market,
the
"simple"
appear to fare too badly.
random
Board
walk
models
In fact, the random
model's predictions had a 32 percent lower bias while only measuring
percent
higher
RMSE.
Table 2 presents
the
wheat
futures
of
walk
11
markets
predictions.
Graphically, the "simple" random walk model appears to consistently
lag behind the market by a small amount (see Figure 3). Since cash wheat
price
in
the time
frame examined
had about the same amount of up and
3.8
3. 7
3. 6
3. 5
3."'
3. 3
3. 2
D 3. 1
0
L 3. o
L 2. 9
A
R 2. B
s 2. 7
I
+ NOMINAL WHEAT PRICE
•
RANDOM WALK FORECASTED PRICE
2. 6
2.5
2."'
2. 3
2.2
2. 1
j
2. 01
I
2
3
5
6
7
B
9
10
11
12
13
15
1e
QUARTERS Cl9B2<CTR1>-19B6<CTR2>l
Figure 3.
Rftndom Walk Model's Forecast versus Cash Price·
17
18
40
down
trends,
explained.
the lower bias of the "simple" random walk model
The random walk model tends to underestimate an
can
be
up-trending
market and overestimate a down-trending market so, if a time frame where
the
up-trending
examined,
the
The
small.
behind
as
However,
period is about equal to the down-trending
bias
of the random walk
model's
consistently as the random walk model's
futures market's price
is
will
be
to
lag
predictions
futures market's price predictions didn't
the
period
predictions
appear
price
had
predictions.
an
occasional
extremely large error (see Figure 4).
Since this study did not establish which statistic of comparison is
of
greater value, any inferences made as to which model is "better" are
left to the reader.
When comparing these two models it must be kept
in
mind that only a short prediction period was analyzed, and that there is
a
definite
cost savings in using the futures market to
predict
price
since this eliminates modeling the PPI.
ARIMA(3,0,3) Model Results
Since the ARIMA(l,O,O) model form of the wheat market is
rejected,
the next step is to identify other ARIMA(p,d,q) model forms that may
more
acf
representative of the wheat market.
Figures 5 and 6
present
and the pact which are the main toots for identification.
rapidly
tails
off
and
the pact cuts off at lag=
3.
Thus,
identification stage, a preliminary model of ARIMA(3,0,0) is
However,
this
model
is rejected at the diagnostic
autocorrelation problems in the residuals.
stage
the
The
act
at
the
indicated.
because
The identification
returned to, and thus the procedure iterates.
be
step
of
is
4.2~
4. 1
4. 0
91
3.
3. 9
3. 7
:~ :1'"'
3. 4
0 3. 3
0
L 3.
L 3. 1
A
21
: :: :j71
+
9
2.
2.
NOMINAL WHEAT PRICE
FUTURES MARKET FORECASTED PRICE
61
2.5
2. 4
2. 3
2. 2
2. 1
2.0\-~~--~-~,_~_,~·r~~--.-~-.~--.-~.--r-.--.-~.--.-.--r-~-r~~r-r-,--r~-.~
2
3
4
5
6
7
8
9
10
11
12
13
14
15
18
QUARTERS [1982<CTR1>-1986CCTR2>l
F1gure 4.
Wheat Futures Market's Forecast versus Cash Pr1ce
17
18
42
LAG COVARIANCE CORRELATION -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
1.85037
1.57016
1.23148
1.05088
0.878363
0.591566
0.35232
0.219312
0.147348
0.00366617
-0.129182
-0.21352
-0.294936
-0.38413
-0.445252
-0.444216
-0.426661
-0.423582
-0.391886
-0.317129
-0.272567
-0.249191
-0.184567
-0.109745
-0.0847079
-0.0877323
-0.0521646
-.00209514
0.0363057
0.0242609
-0.0328679
-0.0586484
-0.0612425
-0.10677
-0.17065
-0.191801
-0.198048
1.00000
0.84857
0.66553
0.56793
0.47470
0.31970
0.19041
0.11852
0.07963
0.00198
-0.06981
-0.11539
-0.15939
-0.20760
-0.24063
-0.24007
-0.23058
-0.22892
-0.21179
-0.17139
-0.14730
-0.13467
-0.09975
-0.05931
-0.04578
-0.04741
-0.02819
-0.00113
0.01962
0.01311
-0.01776
-0.03170
-0.03310
-0.05770
-0.09222
-0.10366
-0.10703
I********************:
:*****************
l*************
l***********
l*********
l******
l****
l**
l**
*
**
***
****
*****
*****
*****
*****
****·
***l
***l
***:
**l
*l
*'
*
*
*
*
*
**
**l
**l
'.'Marks Two Standard Errors
Figure 5.
Autocorrelation Function (ACF) for Cash Wheat
43
LAG CORRELATION -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
0.84857
-0.19483
0.21715
-0.12950
-0.21590
0.03731
-0.01012
0.07198
-0.15443
0.00254
-0.08264
-0.08011
0.00650
-0.04542
0.06273
-0.04855
-0.01333
0.01769
0.00842
-0.03990
-0.00482
0.06038
-0.03827
-0.03405
-0.03357
0.02206
-0.00280
0.05123
-0.08317
-0.12814
0.03920
-0.02338
-0.02867
-0.03198
0.00039
-0.04876
I
I
I
I
I
I
I
I
I
I
I
I
.
l*****************
*****l
I****
·***l
****l
l*
I*
I
I
I
I
·***
I
I
. **
. **
I
I
*
I
I
I
I
l*
*l
I
I
.
I
I
. *l
I
I
I
I
.
.
I
I
I
I
I
I
I
I
I
I
I
I
I
I
.
l*
. **l
·***l
. l*
.
I
I
I
I
l*
*l
*l
*l
.
*l
*'
*l
' ' Marks Two Standard Errors
Figure 6.
Partial Autocorrelation Function (PACF) tor Cash Wheat
44
The ARIMA(3,0,3) form is accepted as satisfactory for the following
reasons:
since
(1)
the estimation stage ARIMA
appear
the coefficients on the AR terms sum to less than one
1983).
and
(2)
the
autocorrelation
the
criterion
residuals
statistic
diagnostic
stage
fulfilled
(Pankratz,
because
the
test on the residuals can't reject the hypothesis
that
are uncorrelated.
is
fulfilled
The test used on the residuals
is
whose approximate distribution is chi-squared under the
hypothesis
that
the residual serjes is white noise
(Pankratz,
a
null
1983).
The exact form of the test used on the residuals is:
a* =
Where
n
is
the
autocorrelation
n
number
cn
of
at lag j,
k
+ 2 > t r2 cj >1 cn - j >
j=l
observations,
Chi
Square OF·
6
0.00 0
5.43 5
8.14 11
11.49 17
= 6,
Prob
Table 3
<------AUTOCORRELATIONS---------------->
0.000 0.020 0.029 -0.031 0.108 -0.126 0.061
0.366 -0.133 0.045 -0.045 0.013 0.031 -0.059
0.701 -0.079 -0.128 -0.015 -0.030 0.051 0.019
0.830 0.035 0.050 0.097 0.068 0.053 0.093
PWt
=a
+ 3'1 02 + 3'2 03 + 3'3 03 + 3'4 073 +
~1 PWt- 1 +~2 PW1::-2
with
estimated
12, 18, and 24.
The general form of the final ARIMA(3,0,3) is:
(18)
the
Autocorrelation Check of Residuals
To
Lag
12
18
24
is
and k can be any positive integer.
presents the results of letting k
Table 3.
r( j)
Ut
= Et
-
}.1
+
~t P~-:s
+ U1::.
Et-1 - X2 Et-2 - X:s Et-:s ·
45
Where PWt-i is the cash price of wheat in the (t-i)th quarter, 02-04 are
seasonal dummy variables
(~contains
the information for 01),
073 is
a
dummy variable for the fourth quarter of 1973 through the second quarter
of 1974,
and Ut represents the error process (MA(3)).
to be estimated by regression
A comparison
model
developed
constitutes
are~.
r,
~.
and A.
of the price predictions made
and
the
wheat
futures
The coefficients
by
market's
the
ARIMA(3,0,3)
price
predictions
efficiency.
The
null hypothesis tested is that the wheat futures is efficient, i.e.
the
wheat
a Fama (1970) semi-strong test for market
futures
forecaster.
market
has
the lowest
bias
and
RMSE
forward
price
The alternative hypothesis is that the wheat futures market
is not the lowest RMSE and bias forward price predictor.
The
general
ARIMA(3,0,3)
model (18) is estimated
over
the
first
quarter 1966 through second quarter 1986 time frame and is then used
recursively
forecast the last 18
to
Whi 1e
quarters of this time period.
recursively forecasting, the model structure is observed to see if model
structure updating would improve fit since structural updating for
fit is allowable in ARIMA modeling, i.e. this study uses an ARIMA
to
forecast price and not to explain structural relationships,
making model updating through time to best fit a necessity.
of
real
model
thereby
The
changing ARIMA model structure through time is also consistent
world behavior since one would expect ARIMA model users to
their model's structure to best fit through time.
best
choice
with
update
The empirical results
of estimating model (18) over the entire period are:
46
PWt
( 19 )
= .4 7 5 3 4
.000000127 02 -.00000000442 03 + .00365 04 +
(3.98)
(2.39)
(1.07)
(2.27)
2.3416 073 + .37671 PWt_ 1
(9.02)
(6.68)
With
Ut
= Et
.28826 PWt_ 2 + .71819 PWt-3 + Ut.
(5.00)
(15.55)
-
- . 50331 Et-1 - 1.0459 Et-2
(11. 88)
(4.02)
~
. 381 71 Et-3.
( 2. 85)
= .94.
Where the variables are as defined for model (18).
The
coefficients
statistically
Since
this
is
coefficient
for
Jess
that
resulted
from
this
estimation
are
all
significant with the exception of the coefficient on
04.
a seasonal model, 04 is kept in as
a
regressor.
estimates and error structure satisfies the ARIMA
criteria
a forecasting model, i.e. the coefficients on the AR terms
than
one. This suggests stationarity; therefore,
the
The
sum
to
hypothesis
that the error structure is uncorrelated can't be rejected (see Table
3
preceding).
Model
empirical
(19) is then used to recursively forecast 18
results
of the shortest model (first
quarter
quarters.
1966
The
through
fourth quarter 1981) are:
(22)
PWt
=
.43498 - .000000129 02 - .00000000194 03 + .003885 04 +
(2.66)
(3.20)
(.340)
(.644)
2.411 073 + .37073 PWt- 1 - .28518 PWt- 2 + .69436 PWt-3 + Ut,
(8.19)
(4.55)
(3.06)
(9.08)
with
Ut=Et- . 48960 Et-1 - 1.7131 Et-2 - .36785 Et-3 •
( 1 • 90)
( 6. 81 )
( 1 • 40)
~
= .98.
Where the variables are as defined for model (18).
The
coefficients obtained from this estimation are all
reasonably
significant with the exception of the coefficients on 03, 04, and
Et_ 3
•
47
The
seasonal dummies, 03 and D4, are left in since this is
model
in
seasonal
and, while removal of the third order MA lag would be permissible
this situation, doing so proved detrimental to model fit.
coefficients
stable
f a i r 1y
on
Since the
to
be
require
fairly
updating
time, the indications are that this model fits this time
frame
we 1 1 .
Forecasts
ahead
the right-hand side variables appeared
through time, and the model structure did not
through
obtained from using the ARIMA£3,0,3) model to
predict, along with the summary statistics
presented in Table 4.
62
a
RMSE
and
one
step
bias,
are
The ARIMA(3,0,3) model's price predictions had a
percent smaller RMSE and a 68.5 percent smaller bias than the
futures
market's price predictions for the first quarter
second
quarter
1986 time frame.
1982
wheat
through
This constitutes a Fama (1970)
semi-
strong rejection of wheat futures market efficiency.
The
ARIMA£3,0,3)
model's forecasts do appear to
lag
the
actual
market price during trends, as did the random walk; however, the size of
the
lags
mode 1
(see
are quite small, thereby explaining the small
Figure ,7).
Other than this s 1 i ght
results of using the ARIMA(3,0,3) model
RMSE
1agg i ng
of
prob 1em,
this
the
for forecasting are quite good.
Caution needs to be taken when interpreting these results as they relate
to the quality of the ARIMA(3,0,3) model as a forecaster of wheat prices
over longer or other time frames since this model was fit for this
time
period and may not perform as well in other time periods.
A discussion of the potential incremental returns from
speculating
with this model will be presented in the final section of this chapter.
48
Table 4.
Price Predictions with an ARIMA(3,0,3) Model
Time Period
1982
1982
1982
1982
1983
1983
1983
1983
1984
1984
1984
1984
1985
1985
1985
1985
1986
1986
I
II
III
IV
I
II
III
IV
I
II
II I
IV
I
II
II I
IV
I
II
Cash Price
Prediction
Residual
3.59
3.31
3.18
3.23
3.36
3.53
3.62
3.55
3.57
3.51
3.47
3.49
3.58
3.27
2.83
3.46
3.40
2.52
3.57
3.36
3.24
3.16
3.24
3.36
3.54
3.54
3.52
3.41
3.43
3.47
3.49
3.25
3.01
3.24
3.30
2. 72
-0.02
0.05
0.06
-0.07
-0.12
-0.17
-0.08
-0.01
-0.05
-0.10
-0.04
-0.02
-0.09
-0.02
0.18
-0.22
-0.10
0.20
RMSE = .1092907
Bias = -3.444443E-02
3. 2
3. 1
D 3. 0
0
L 2. 9
L
A 2. 9
R
s
+ NOMINAL WHEAT PRICE
•
2. 7
Jl,
"'
ARMA <3. 3> FORECASTED PRICE
2. 6
2. 5
2."
"l
2. 2
2.
2. I
~
2. 0 i
I
2
3
4
5
6
7
8
9
10
11
12
13
14
15
QUARTERS C1982CCJTR1>-1986<CJTR2>J
Ftgure 7.
ARIMA(3,0,3) Model's Forecast versus Cash Prtce
16
17
18
50
USDA Model Results
··1
t
The
the
first structural model that this study examined is based
genera 1 USDA mode 1 (11 ) .
right-hand
upon
The term "based upon" means that the same
side variables as those found in model
the model that is used for the efficiency test.
(11)
are
present
in
However, lag lengths on
the right-hand side variables and error structure are adjusted to obtain
best
fit.
This is justifiable because the prediction periods
and
data series time frame used in this study are different from those
by the USDA studies.
proposed
by
Any general postulated cause/effect
the general USDA model
(11)
will be
only the lead/lag time relationships and
will
(changes are limited to those which improved
change
used
relationships
unaffected
adjustments;
the
by
error
these
structure
model
The changes made resulted in the following general model form
fit).
(referred
to hereafter as the USDA model):
4
( 21 )
PWt =a+ /3PWt_ 1 +.:E
J=1
with
C1
D1 (U/S)t_ 1 + Ut,
Ut = Et - A1 Et-1 ·
Where PWt_ 1 is the cash price of wheat in the (t-i)th time period, D1 is
a
I
f,
dummy
through
(U/S)t-1
variable representing the (i)th quarter (i=1 for
March quarter,
is
the
January
i=2 for the April through June quarter,
the quarterly use-to-wheat ending stocks ratio
etc.),
lagged
time period, and Ut is the error structure (MA(1)).
match
the
USDA's results by estimating the model over the same time period as
the
The
one
used
first step taken with this model is
an attempt to
by Westcott et al (1984), i.e. 1971 through 1983.
An
exact
51
match
is
not expected since Westcott et al. (1984)
did
not
identify
exactly what wheat series they were working with and it is unlikely that
it was number 2 soft red winter wheat nor; did they publish exactly what
error structure is used in their model.
= .619
+ .400 PWt- 1 + 3.937 D1 (U/Slt- 1 +
(2.74) (2.74)
(2.44)
PWt
(22)
The model form obtained is:
7.289 D3 (U/S)t-1 +
(3.90)
with
Ut
= Et
6.836 D2 (U/Slt-1 +
(4.30)
6.409 D4CU/S)t-1 + Ut,
( 2. 87)
- . 731 Et -1
,
(5.17)
1(2
While
the
coefficients of model (22) don't exactly match those of
USDA model (12),
fit
is
= . 85.
the
the coefficients of model (22) are significant and the
reasonable
for
a
structural
model, thereby
justifying
the
relationships proposed by Westcott et al. (1984) for this time frame.
A comparison of the price predictions made by USDA model (21)
price
predictions made by the wheat futures market constitutes
(1970)
semi-strong test of market efficiency.
that
the
bias
forward
market.
The null
a
hypothesis
wheat futures market is efficient, i.e. the lowest
price prediction available is made by the
wheat
RMSE
and
Fama
is
and
futures
The alternative hypothesis is that the wheat futures market
is
not efficient, i.e. the lowest RMSE and bias forward price predictor
is
not the wheat futures market.
USDA
2nd
quarter
quarters
Since
model (21) is estimated over the first quarter
in
these
1966
1986 time frame and then used to recursively
order to obtain forward price predictions
predictions are in real values they have
forecast
(real
to
through
be
18
values).
changed,
52
using the predicted PPI, to nominal values.
As this model is based uoon
relationships among variables, no structural updating
proposed
time is considered.
(23)
PWt
through
The empirical results of estimating model (21) are:
= .68055(1.90)
.11830 Dl(U/S)t- 1 + 1.7466 D2(U/S)t_ 1 +
(.1387)
(2.248)
1.5797 03(U/5Jt_ 1 + .77304 D4(U/S)t_ 1 + .75023 PWt_ 1 + Ut,
(1.75)
(.655)
(7.87)
with
Ut
= Et
- . 46252 Et-1 ,
(3.94)
R2
= .82.
Where the variables are as defined for model (21).
The
coefficients
disappointing.
D2CU/S)t_ 1
,
Only
obtained
from estimating this
model
two of the right hand-side variables,
have coefficients that are statistically
are
PW t- 1 and
significant.
low significance of the coefficients is reflected in the marginal
fit as defined by the R2 statistic.
very
The
model
Clearly the extended time frame
of
first quarter 1966 through second quarter 1986 is not modeled as well by
(
this structural model as is the shorter time frame of first quarter 1971
through
first
quarter
1983.
This indicates
that
the
relationships
(model (21)) proposed by Westcott et al. (1984) may be a function of the
period
of time for which the market is examined.
model
is
wheat
market, it is used to forecast wheat price.
results
va I ues).
However,
since
one that USDA publications present as representative
of
of
this
the
Table 5 presents the
this forecast (predictions have been converted
to
nominal
53
Table 5.
Price Predictions with Model (23)
Time Period
1982
1982
1982
1982
1983
1983
1983
1983
1984
1984
1984
1984
1985
1985
1985
1985
1986
1986
Cash Price
Prediction
Residual
3.59
3.31
3.18
3.23
3.36
3.53
3.62
3.55
3.57
3.51
3.47
3.49
3.58
3.27
2.83
3.46
3.40
2.52
3.72
3.26
3.86
3.39
3.25
3.23
3.96
3.84
3.49
3.41
3.97
3.90
3.39
3.52
3.39
3.05
3.58
3.17
0.13
-0.05
0.68
0.16
-0.11
-0.30
0.34
0.29
-0.08
-0.10
0.50
0.41
-0.19
0.25
0.56
-0.41
0.18
0.65
I
II
III
IV
I
II
III
IV
I
II
II I
IV
I
II
III
IV
I
II
RMSE
Bias
= .3559516
= .1621556
Model (23)'s price predictions have a 24 percent larger RMSE and
35
percent
predictions;
that
I -
larger
bias
than
the
wheat
therefore, this model cannot
the wheat futures market is efficient.
predictions
made
market's
futures
reject the
null
Examination of
by model (23) reveal large swings
in
the
price, thereby indicating model instability (see Figure 8).
a
price
hypothesis
the
price
predicted
While
this
model may have adequately explained the first quarter 1971 through first
quarter
1983 time frame, it certainly can't be advocated tor the
quarter 1966 through second quarter 1986 time frame.
first
"'· 0
3. D
3.8
3. 7
3. 6
3.5
3."'
3. 3
0 3. 2
0
L 3. 1
.
L 3.0
A 2. D
R
s 2.8
U1
+ NOMINAL WHEAT PRICE
•
2.7
USDA MODEL FORECASTED PRICE
QUARTERS C1982CQTR1>-1986CQTR2>l
Figure B.
USDA Hodel's Forecast
versus Cash Price
55
Market Trader's Model
The
next
"based upon•
obtained
Resul~s
structural model is "based upon• model (13).
is· defined as discussed earlier.
after
adjustments
The
exact
is (referred to hereafter
as
The
term
model
form
the
market
trader's model):
(24)
PWt = a + /102 + /103 + /104 + /1073 +
CC::z(U4/S) + a1 (PW/PC>t- 1 +
With
Where
Ut = Et -
A2
-
Et_ 2
-
Ut,
A3
Et-::s.
representing
March, i=2
the
representing
average
total
1974
time
frame,
(U4/S)t_ 1
ratio in time period t-1 of the tour
wh~at
the
is
intercept
a
seasonal
January
through
April through June, etc.), 073 is a dummy variable
through
the
01
the (i)th quarter (i=1 represents
repres~nts
1973
a is
seasonal effects of quarter 1),
~he
I
dummy
tor
Et- 1
(U4/S lt- 1 +
PWt is the price of wheat in time period t,
(contains
term
A1
CX:1
is
a
variable
quarter
use to total wheat ending stocks , (PW/PC>t-l is
variable
representing the ratio in time period t-1 of cash white
to
corn (corn and wheat price are deflated by the
cash
moving
PPI),
a
wheat
and
ut
represents the error structure(MA£3)).
A comparison
trader's
represents
of
the
results of
price
predicting
with
market
model (24) and price predicting with the wheat futures
market
a Fama (1970) semi-strong test of market efficiency.
Again,
the null hypothesis is that the wheat futures market is efficient,
i.e.
the wheat futures market has the smallest RMSE and bias price forecaster
versus the alternative hypothesis that the wheat market is
i.e. not the smallest RMSE and bias price forecaster.
inefficient,
56
Market trader's model (24) is estimated over the first quarter 1966
.through
second
quarter 1986 time frame and then
used
to
recursively
forecast 18 quarters in order to obtain real price predictions.
these
real price predictions are converted to nominal values using
predicted
for
PPI values.
variables.
t~
the
considered
Structural updating over time isn't
this model since it was designed
(25)
Again,
represent a relationship
among
The empirical results of estimating this model are:
= 1.7231-
PWt
.39668 02- .58775 03 -.056751 04 + 4.0399 073 +
(2.65)
(2.66)
(.247)
(9.18)
(3.05)
1.7048 (U4/S)t_ 1 + 1.3028 (U4/S)t_ 2 +.99146 (PW/PC>t-1 + Ut,
(4.01)
(3.06)
(2.70)
with
= Et
Ut
- . 44048 Et_ 1 - . 33002 Et-2,
(3.36)
(2.70)
= .90.
~
Where the variables are as defined for model (24).
The
coefficients
exception
model
of
on
this
model are
all
the coefficient on seasonal dummy
appears
to
significant
04.
be much more structurally sound
with
This
than
structural
the
previous
structural model (model (23)); model (25) fits this wheat data
time
frame relatively well as is indicated by
suggesting
the~
set
that the variable relationships proposed by Schwager
presents
the
one
step
ahead
forecasts
and
statistic, thereby
are fairly sound, at least for the period examined by this study.
6
the
obtained
by
(1984)
Table
recursively
forecasting with model (25) and then converting the real price values to
nominal
values.
The summary
presented in Table 6.
statistics, RMSE
and
bias,
are
also
57
Table 6.
Price Predictions with the Market Trader's Model
Time Period
1982
1982
1982
1982
1983
1983
1983
1983
1984
1984
1984
1984
1985
1985
1985
1985
1986
1986
I
II
III
IV
I
II
III
IV
I
II
III
IV
I
II
I II
IV
I
II
Cash Price
Prediction
3.59
3.31
3.18
3.23
3.36
3.53
3.62
3.55
3.57
3.51
3.47
3.49
3.58
3.27
2.83
3.46
3.40
2.52
3.98
3.63
3.67
3.71
3.50
3.35
3.59
3.96
3.64
3.57
3.64
3.96
3.87
3.60
3.43
3.28
3.67
3.28
RMSE
Bias
Residual
0.39
0.32
0.49
0.48
0.14
-0.18
-0.03
0.41
0.07
0.06
0.17
0.47
0.29
0.33
0.60
-0.18
0.27
0.76
= .3617189
= .2686888
Model (25)'s price predictions have a 28 percent larger RMSE and
a
123 percent larger bias than price predictions made by the wheat futures
market.
Model
(25l's
performance is not good
enough
hypothesis that the wheat futures market is efficient.
market
trader's
examined
Figure 9).
since
to
reject
the
Model (25),
the
model, is by far the worst biased model of
it consistently overestimated market wheat
the
price
group
(see
In fact, out of 18 quarters of price predictions, model (25)
only underestimated market price three times.
Clearly, model (25) isn't
a good choice for use as a price prediction model.
4.0~
3.9
3.
e1
'
3. 7
3.
s
3. 5
3. 4
3. 3
D 3.2
0
L 3. 1
L 3.0
A
R 2. 9
s
Ul
to
2. 9
+ NOMINAL WHEAT PRICE
2. 7
•
FUTURES MODEL FORECASTED PRICE
2. 6
2.5
2. 4
2. 3
2.2
2. 1
2.0 ~,-,--r-.~-.~r-r-~,-~-r~-.~r-r-~~,-~-r-r~~--r-r-~,-~-r-r-r~-T
2
3
4
5
s
7
e
9
10
11
12
13
14
15
16
QUARTERS [1992<CTR1>-198S<CTR2>l
Figure 9.
Market Traders Hodel's Forecast versus Cash Price
17
19
59
Predicting the PPI
An
step
ARIMA approach is taken to build a model that would
ahead
deflate
The actual PPI data
used
to
the price variables in the structural models (23} and
(251
is
The result of this process
is
to ARIMA modeling techniques.
an ARIMA(l,O,O) model of the PPI.
is
able
need
fact
(Again the statistical package DYNREG
to handle the slight trend in the data thereby,
to difference.)
random
negating
that the PPI series turned out to be a random walk is
deflating
the
This model form defines the PPI data series as
walk with a positive drift of about 3.5 percent per
because
one
series
subjected
forecast of the PPI.
yield
price
data
series with
introduce new serial correlation problems.
(26)
PPit = a +
with
PPI
The
encouraging
series
doesn't
The general model form is:
PPit- 1 + Ut,
{3
Ut
this
year.
a
= Et.
Where PPit-:1. is the PPI in the (t-i )th time frame,
and ut is the
error
process CMA£0)).
This model is estimated over the 1966 through 2nd quarter 1986 time
frame.
PPI
predictions
forecasting 18 quarters.
be
used
to
predictions
convert
made
to
are obtained from this
model
nominal
price
predictions
by the structural models examined.
PPit
= .012949
(1.80)
with
recursively
These forecasted values are the ones that will
form obtained from the estimation is:
( 27)
by
+ .. 99243 PPit- 1 + Ut,
(103.51)
ut =
~\
.i!.
the
The
real
price
exact
model
60
Table 7
presents the predictions generated by this model.
Table 7.
PPI Predictions with a Random Walk Model
Time Period
Actual PPI
Prediction
1982
1982
1982
1982
1983
1983
1983
1983
1984
1984
1984
1984
1985
1985
1985
1985
1986
1986
97.21
100.27
97.21
96.15
98.43
99.18
101.77
101.30
105.22
103.22
101.96
101.81
100.00
97.84
94.62
99.21
97.13
98.11
95.80
98.47
101.29
98.12
97.12
99.39
100.22
102.74
102.41
106.19
104.08
102.78
102.52
100.62
98.34
95.26
99.74
97.69
I
II
III
IV
I
II
II I
IV
I
II
III
IV
I
II
III
IV
I
II
Utilizing the ARIMA(3,0,3) Model
The
(1970)
ARIMA(3,0,3) model's forecasts succeeded in obtaining
semi-strong
pointed
out
necessary
the
by
form rejection of market efficiency.
Rausser and Carter (1983), this
However,
represents
only
conditions for general market efficiency rejection.
sufficiency
c~nstructing
incremental
requirements
and
utilizing
risk
adjusted
for efficiency rejection,
the
ARIMA(3,0,3)
section
not
exceed
the
meet
of
the
model.
A
discussion of returns to price speculating with this model will also
be
of the costs of building and utilizing
will
cost
as
to
some
This
the
To
Fama
attempt
quantify
benefits.
must
a
this
61
presented;
however,
risk
wheat
price
adjustment of the returns
is
left
to
the
reader.
Since
straightforward,
build.
an
and
ARIMA
ARIMA(3,0,3) model is
procedures
relatively
spent building this
running
the
that
model is estimated at $1000.
is assumed to be zero.
next
step
house
more
wheat
However, an adverse price
have
a
an
be
margin
brokerage
movement
would
Since
initial
of
be
one
cash
the first quarter 1982
quarter 1986 time period was $.88 ($4400),
second
to
approximately $15,000 and the maximum
price change for any given quarter in
to
cost. of
The minimum
required than $750 to hold the average contract one quarter.
of wheat is worth
of
$1500.
than $.05 would result in margin calls, i.e. more money
contract
close
total
to trade one wheat contract (5000 bushels) at
approximately $750.
is
the
is to determine how much money would
invested to utilize this model's price predictions.
requirement
time
The marginal cost
Therefore,
to
reestimating
ARIMA(3,0,3) model once it is constructed is so
it
quite
$500 and the opportunity cost of the
building and running this model is estimated to be
The
are
inexpensive
Computer charges for the time spent estimating and
this model are approximately
zero
data
to
margin
amount of $5000 is deemed sufficient.
The
total cost of building and opening an account to operate
model sums
half
years
alternative
four
to $6500.
if
the
year period.
This model would have been utilized four and onetest prediction period
for this
this
is
~atched.
The
"safe"
$6500 would be to invest it in a bank CD for
If this were done with a 10 percent
interest
the
rate,
62
the amount in the account at the end of four and one half years would be
$9981.15.
Assume,
that
ARIMA(3,0,3)
the
first
trading
(18
CD,
the
model is built to be used as a price speculation tool
for
quarter 1982 through second quarter 1986 test
a
period.
rule that will be followed with one wheat contract per
trades) will be:
prediction
t+l
now, rather than investing the money in
futures
held
until
contract
ARIMA(3,0,3) model's price
maturity
is
reached.
price
market's
price prediction, then one (long) wheat futures contract
maturity will be purchased , i.e. a "long" position will be
and
quarter
If, in quarter t, the ARIMA(3,0,3) model's
for quarter t+1 is greater than the wheat
with
contract
position
will
instead,
If,
Table
reached.
established
8
the
prediction for quarter t+l is less than
with t+l maturity will be purchased, i.e.
be
t+l
established
wheat futures market's price prediction for t+l, then one (short)
futures
The
and held
until
contract
presents the quarterly breakdown
of
a
the
wheat
"short•
maturity
earnings
is
and
losses that are obtained from following this rule.
The
gross
commission
recalculated
return
$70
of
at
for
trading this
model
per trade is charged, then
$15,990.00.
is
the
$17,250.
gross
If
return
Assuming that no interest is paid on
a
is
the
brokerage house's accounts and that no money is removed from the account
to
be invested elsewhere, the total brokerage account dollar
the end
value
at
of the trading period would be $20,9900 (including the original
amount invested).
It is pertinent to note at this point that the previous assumptions
are
quite restrictive, but the intent was to assume the worst
possible
63
investment scenario.
In reality, most brokerage accounts pay interest,
and, even if the brokerage account did not pay interest, any money above
margin
could
interest
increasing
be
removed
bearing
the
account.
from the brokerage firm
There
also
existed
and
placed
the
in
an
possibility
of
number of contracts traded per quarter as
the
account
value grew, thereby increasing returns.
Table
8.
Time
Period
1982
1982
1982
1982
1983
1983
1983
1983
1984
1984
1984
1984
1985
1985
1985
1985
1986
1986
I
II
II I
IV
I
II
III
IV
I
II
III
IV
I
II
III
IV
I
II
The
Returns to Market Price Speculation
Model
Cash
Price
3.59
3.31
3.18
3.23
3.36
3.53
3.62
3.55
3.57
3.51
3.47
3.49
3.58
3.27
2.83
3.46
3.40
2.52
ARIMA(3,0,3)
Model's
Prediction
3.57
3.36
3.24
3.16
3.24
3.36
3.54
3.54
3.52
3.41
3.43
3.47
3.49
3.25
3.01
3.24
3.30
2. 72
Using
Futures
Market's
Prediction
the
ARIMA(3,0,3)
Position
Established
4.20
3.66
3.58
3.47
3.37
3.45
3.58
3.95
3.55
3.44
3.62
3.52
3.47
3.36
3.28
2.93
3.43
2.78
5
5
s
5
5
s
s
s
5
5
s
s
L
s
s
L
5
5
Return
3050.00
1750.00
2000.00
1200.00
50.00
- 400.00
- 200.00
2000.00
- 100.00
- 350.00
750.00
150.00
550.00
450.00
2250.00
2650.00
150.00
1300.00
resulting return to speculation is 19.5 percent per year
with
the restrictive approach taken.
risk
adjustment
Clearly there now needs to
made to compensate for the fact that
using
an
even
be
a
ARIMA
64
model
to
trade
is quite risky.
As to the exact extent
of
the
adjustment, no comments will be made since risk adjustment is a
of
personal judgment.
real
return
after
subject.
If the risk adjustment is large enough that
risk
adjustment to speculation
is
Jess
risk
than
the
1~
percent, then sufficiency criterion for efficiency rejection will not be
met; however,
obtained,
wi 11
be
if a risk adjusted return of greater than 10
then
No matter what the conclusion
met.
criterion
sufficiency criterion for market
is
percent
efficiency
on
the
is
rejection
sufficiency
requirements, it must be remembered that this conclusion
may
only be valid for the time period examined by this study.
Another
potential
returns
common
above
taken
in
the
literature
average returns to a trading rule is
generated
strategies.
approach
by
using the trading rule to
to
naive
to
examine
compare. the
buy
and
hOld
Following a naive buy and hold strategy for this 18 quarter
time period results in a $10,850 loss.
per trade, this Joss become $12,110.
With
a commission charge of $70
Clearly, for this time period, the
ARIMA(3,0,3) model's speculative approach is superior to a naive buy and
hold strategy.
hold
wheat
If,
However, the relatively poor performance of the buy
and
strategy can at least partially be explained by the fact that
the
market's general overall trend was down in the
period
examined.
instead, a naive sell and hold strategy is followed, the
resulting
return would be exactly opposite, i.e. a
$10,850 profit is generated by
a naive sell and hold strategy (with commission this is a
No matter which naive strategy is followed,
from using the ARIMA(3,0,3) is still superior.
ARIMA
model
$9590).
the speculative return
This indicates that
is capturing some relevant information which
allowed
the
for
65
better than naive performance.
a
Fama (1970)
problem
of
judgment
semi-strong
These results fit into the framework
market efficiency rejection;
however,
different risks for different strategies again
of whether sufficiency criteria for efficiency
the
prevents
rejection
of
a
are
met.
The
model,
general conclusion of this empirics chapter is that
the
rejection
sufficiency
ARIMAC3,0,3),
of
market
criteria
fully met the criteria
efficiency.
for
As for
efficiency
whether
rejection,
for
a
this
only
only
one
Fama
(1970)
model
meets
conditional
conclusions can be made because of the problems with ranking risk.
66
CHAPTER 4
SUMMARY AND CONCLUSIONS
This
chapter
briefly
summarizes
section
discusses
this
study.
is broken into three sections.
the
steps undertaken by this
The
first
study.
any conclusions made from the results
The third section presents some suggestions
section
The
second
obtained
for
by
further
research.
Summary
Futures
market efficiency is of concern to both market traders and
non-market participants since it relates the performance of a market
allocating
market
resources
A problem exists in
what
characteristics are consistent with market efficiency are
obtuse,
i.e.
the tests taken for market efficiency are often limited to testing
only
one
hypothesis
rejected.
its
particular definition of efficiency and have
the particular definition chosen.
of
for
for
exactly
Board
because the precise criteria
testing
defining
beyond
efficiency
through time.
in
Chicago
see
if
the
could
be
Fama (1970) approach to efficiency was taken because
of
wheat
In this study,
futures market was examined
of market efficiency,
to
as defined by Fama (1970),
popularity in the relevant literature and because of its
defined tests.
meaning
the
Trade's
The
little
concisely
67.
The first step of this study was to determine if the quarterly cash
wheat
market
hypothesis
Fama
followed
a
random walk model.
The
rejection
of
the
that the cash wheat market follows a random walk provided
~orm
(1970) weak
possibility
of
rejection of market efficiency and indicated
developing an ARIMA model other than
the
a
the
ARIMA(l,O,Ol
model to forward predict price.
The
subsequent steps that were taken in this study all find
basis in the concept that,
their
if a forward price predicting model is shown
to forecast future price "better" than the relevant futures market, then
this constitutes a Fama (1970) semi-strong market efficiency
The
rejection.
models that were used in this study were either built through ARIMA
modeling procedures or selected from publicly available literature.
Box
followed
wheat
and
to
Jenkin's
(1976) ARIMA(p,d,q)
modeling
procedures
create an ARIMA(3,0,3) model of the quarterly
market.
The
ARIMA(3,0,3)
model was used
to
one
were
cash
price
step
ahead
forecast wheat prices for the first quarter 1982 through second
quarter
1986
on
basis
time
frame.
The price forecasts obtained were compared,
of RMSE and bias, to price predictions made by the Chicago
of Trade's wheat futures market.
the
Board
A Fama (1970) semi-strong rejection of
market efficiency was obtained on the basis of these comparisons.
Two
the
other forward wheat price predicting models were
relevant literature in order to compare, on the basis of
bias, their forward price predictions
wheat
chosen
RMSE
to the Chicago Board of
futures markets forward price predictions.
from
Although both
Trade's
models
enjoy some popularity in the literature, neither was able to reject
hypothesis that
the Chicago Board of Trade's wheat future's
and
market
the
is
68
efficient.
creators
market
This
of
can
be
partially explained by
these models were probably as
structural
relationships
as
they
the
fact
concerned
were
with
with
that
the
explaining
forward
price
prediction.
Since Fama•s 1970 work on efficiency is dated, this study undertook
a
final
step
to
see if any conclusions
on
a
later
definition
of
efficiency could be obtained, i.e. a Fama (1970) rejection of efficiency
represented
p
only
the
efficiency rejection,
market
efficiency.
efficiency rejection,
result,
this
rejection
of
the
necessary
conditions
for
and is not sufficient for a general rejection
To
meet
the
sufficiency
criteria
for
costs and risk have to be accounted
study simulated price speculation with
market
for.
the
of
As
a
ARIMAC3,0,3)
model for the first quarter 1982 through second quarter 1986 time frame.
A 19.5
percent
after cost rate of return
ARIMA(3,0,3) for this time period.
of
risk
level
was
obtained
risk
in
the
There is, however, a certain amount
involved in using an ARIMA model to forecast
of
by
using an ARIMA model to forecast
price,
price
and
the
cannot
be
assumed equal to the level of risk faced by users of the futures market.
As a result,
adjusted
for
the returns generated by the ARIMA(3,0,3) model need to be
risk
before they are compared to
"safe" investments such as cos.
generated
by
However, this study did not determine a
satisfactory way to adjust for risk
preferences
returns
that would reflect individual
risk
and the risk of using ARIMA models to forecast price.
Not
adjusting for risk made impossible any conclusions concerning whether or
not
the
sufficient
conditions for
market
efficiency
defined by Rausser and Carter (1983), were met.
rejection,
as
69
Conclusions
Since efficiency studies are based only on a particular
ana/or
test
subject
of
efficiency, any general conclusions
to limitations.
definition
reached
will
This results in the tendency of rejecting
the
hypothesis of market efficiency when, in fact, the market may really
"efficient."
implications
a
As
of
the
result
of
the
previously
be
problems,
stated
wheat market efficiency rejection
be
that
will
subsequently presented are limited, and should not be inferred to
be
imply
more tha·n the fact that a potent a 1 problem may exist.
For the first quarter 1982 through second quarter 1986 time
period
this study was able to reject the hypothesis of. market efficiency.
This
implies
been
that
some
objectionable resource allocations
present during this time frame.
may
have
For example, farmers who based planting
decisions on the Chicago Board of Trade's forecast of future wheat price
could
potentially
production,
future's
Chicago
i.e.
market
resources
have been misallocating too many resources to
the
$.12 positive bias found to exist in
Board
the
throughout this time period may have caused
to be allocated to wheat production.
of
Trade's
wheat
futures
wheat
wheat
too
many
The large RMSE of
market
(relative
the
to
the
ARIMA(3,0,3J model's RMSEJ also indicates that the through time resource
allocations
futures
initiated because of the forward price predictions
market
allocations
were
consistently
more
inaccurate
than
of
resource
based upon the price predictions of the ARIMA(3,0,3)
would have been.
the
model
70
As
to
whether the resource misallocations
that
are
potentially
indicated by this study are just a function of the type of tests used or
the time period
price
ex~mined,
speculation
exist.
The
little can be said.
is risky,
Information is costly and
so perhaps no objectionable
wheat futures markets have,
inaccuracies
for approximately 100
years,
provided a forward forecast of price at low cost to the user, and cannot
be assigned the label of "inefficient"
than
was presented here.
Fama
(1970)
probability
without a great deal more
This study claims only to have rejected
definition of efficiency,
that
proof
objectionable
thereby indicating
inaccuracies
do exist
the
in
the
slight
the
wheat
futures market.
Further Research
Even though the very definition of the word efficiency is obtuse to
economists,
and
bias
being
the
analysis of futures markets on the basis of
offers important contributions as to how well
allocated.
forecast
resources
are
This study looked at but one futures market and
one
There exist many markets and many
length.
variance
forecast
lengths
that could benefit from some examination as long as the results from the
examinations are taken at face value and not used to infer too much.
Some
undertaken
predictions
lagged
specific
research
that
this
author
would
includes: (1) extension of the length of the
of
the wheat market to see at which
like
to
forward
forecast
length
price terms quit revealing market stickiness, i.e. finding
forecast length
could
be
see
price
the
what
appropriately represented with a random walk
model; (2) tests to see if any significance can be placed on price chart
71
pattern
formations that are advocated by technical market
price prediction tools; (3) development of
takes
into
thereby
test for efficiency
account the risks of using trading rules to
allows
received
a
an
analysts
accurate measurement of the
risk
by speculators; and (4) measurements based on
as
that
speculate
and
adjusted
return
actual
trading
records of whether speculators, as a group or individually, can forecast
price.
hence
explain
If
earn
why
speculators are shown to be unable to
forecast
below average returns, then research needs to
"rational"
individuals
consistently losing endeavor.
chose
to
price
be
participate
and
done
to
in
a
....CDCD
r....
0
G'l
:0
~
"C
:X:
-<
....,
""
73
BIBLIOGRAPHY
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Schwager, J.D. A Complete Guide to the Futures Markets: Fundamental
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Prices.·
American
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)>
"'0
"'0
m
z
0
X
77
Table 9.
Date
1966
1966
1966
1966
1967
1967
1967
1967
1968
1968
1968
1968
1969
1969
1969
1969
1970
1970
1970
1970
1971
1971
1971
1971
1972
1972
1"972
1972
1973
1973
1973
1973
1974
1974
1974
.1974
1975
1975
1975
1975
1976
1976
I
II
II I
IV
I
II
III
IV
I
II
II I
IV
I
II
I II
IV
I
II
II I
IV
I
II
III
IV
I
II
III
IV
I
II
III
IV
I
II
III
IV
I
II
I II
IV
I
II
Original Data Set
PPI
Cash
Wheat
Total
Use
39.04
39.12
39.55
39.20
39.12
39.36
39.3239.55
40.06
40.26
40.38
40.65
41.36
41 .91
42.07
42.62
43.17
43.32
43.60
43.60
44.38
44.89
44.97
45.33
46.11
46.66
47.21
48.27
50.98
53.42
54.87
55.70
59.47
61.15
65.67
67.36
66.93
68.22
69.80
70.19
70.54
71.92
1.63
1. 79
1.86
1.80
1.80
1.58
1. 51
1.46
1.50
1. 30
1.20
1. 33
1. 32
1.28
1. 31
1.48
1. 53
1. 41
1.64
1.68
1.63
1. 52
1. 58
1.65
1.67
1". 61
2.02
2.60
2.37
2.82
5.11
5.84
5.59
3.91
4.41
4.60
3.62
3.03
4.06
3.32
3.66
3.47
419.00
382.40
411.40
387.60
349.20
275.40
388.20
347.40
372.90
300.40
430.90
339.40
233.60
294.20
403.90
341.70
337.60
314.10
870.80
378.70
349.90
237.90
568.10
326.30
337.30
227.50
659.10
472.20
472.10
330.40
856.80
523.60
380.50
209.60
562.00
455.20
445.80
227.30
676.70
500.00
449.60
272.40
Ending
Stocks
Moving
Average
Use
Cash
Corn
917.30
535.20
1435.60
1049.10
700.10
425.00
1559.30
1212.10
839.50
539.40
1684.90
1345.70
1112.40
818.60
1875.20
1534.50
1197.70
884.70
1731.60
1410.00
1060.40
822.80
1873.80
1547.60
1210.70
983.40
1870.90
1399.00
927.30
597 .1 0
1451.60
928.30
548.10
340.10
1562.10
1107.50
662.10
435.00
1885.80
1386.60
937.40
665.60
000.00
000.00
000.00
400.10
382.56
355.90
350.10
340.05
345.98
352.22
362.90
360.90
326.07
324.53
317.78
318.35
344.35
349.33
466.05
475.30
478.38
459.32
383.65
370.55
367.40
364.80
387.55
424.02
457.72
483.45
532.87
545.72
522.82
492.62
418.92
401.82
418.15
422.57
451.25
462.45
463.40
474.67
1.19
1.20
1. 32
1.28
1. 27
1 .26'
1.15
1.02
1.06
1.07
1. 01
1.02
1.09
1.16
1.17
1.09
1.13
1.18
1. 30
1.33
1. 43
1. 41
1.22
1.02
1.09
1.14
1.16
1.27
1. 37
1.67
2.29
2.25
2.68
2.48
3.19
3.35
2.86
2.67
2.81
2.44
2.47
2.60
78
Table 9.
Date
1976
1976
1977
1977
1977
1977
1978
1978
1978
1978
1979
1979
1979
1979
1980
1980
1980
1980
1981
1981
1981
1981
1982
.1982
1982
1982
1983
1983
1983
1983
1984
1984
1984
1984
1985
1985
1985
1985
1986
1986
III
IV
I
II
III
IV
I
II
II I
IV
I
II
I II
IV
I
II
II I
IV
I
II
II I
IV
I
II
II I
IV
I
II
II I
IV
I
II
III
IV
I
II
III
IV
I
II
Continued
PPI
Cash
Wheat
Total
Use
Ending
Stocks
Moving
Average
Use
Cash
Corn
72.55
73.49
74.98
75.22
72.27
74.43
78.55
82.64
82.29
84.88
89.95
89.95
91.04
92.14
92.26
92.03
100.67
100.75
99.57
99.88
98.31
94.66
97.21
100.27
97.21
96.15
98.43
99.18
101 .71
101.30
105.22
103.22
101.96
101.81
100.00
97.84
94.62
99.21
97.13
98.11
2.89
2.66
2.63
2.29
2.20
2.65
2.82
3.18
3.42
3.68
3.79
4.36
4.28
4.26
4.18
3.96
4.38
4.54
4.15
3.60
3.87
3.86
3.59
3.31
3.18
3.23
3.36
3.53
3.62
3.55
3.57
3.51
3.47
3.49
3.58
3.27
2.83
3.46
3.40
2.52
624.90
407.20
393.00
278.80
755.10
407.90
467.50
352.40
820.00
503.60
401.90
305.60
788.10
555.10
491.60
323.50
810.20
569.90
575.80
340.40
1074.70
556.20
621.30
392.70
956.10
466.30
646.90
347.60
981.20
629.70
569.40
360.30
1258.80
601.90
475.10
243.70
885.00
450.30
397.90
227.90
2190.40
1783.60
1390.90
1113.20
2404.50
1997.00
1529.90
1177.80
2133.90
1630.80
1229.40
924.10
2270.80
1716.20
1225.10
902.00
2473.50
1903.80
1329.10
989.10
2727.50
2172.10
1551.20
1159.40
2969.50
2506.10
1862.00
1515.10
2955.20
2326.40
1758.10
1398.60
2467.00
2139.80
1667.10
1425.20
2971.10
2536.40
2130.10
1905.00
461.72
438.52
424.37
425.97
458.52
458.70
477.32
495.72
511.95
535.87
519.47
507.77
499.80
512.67
535.10
539.57
545.10
548.80
569.85
574.07
640.20
636.77
648.15
661.22
631.57
609.10
615.50
604.22
610.50
651.35
631.97
635.15
704.55
697.60
674.02
644.87
551.42
510.62
494.23
490.52
2.69
2.20
2.34
2.23
1. 70
1.84
2.06
2.27
2.05
2.03
2.17
2.37
2.56
2.35
2.41
2.42
2.89
3.09
3.22
3.22
2.85
2.39
2.48
2.57
2.45
2.12
2.54
3.01
3.27
3.16
3.16
3.34
3.11
2.59
2.64
2.67
2.44
2.20
2.31
2.34