Estimation of the US Treasury Yield Curve at
Daily and Intra-Daily Frequency∗
Lawrence R. Klein
Benjamin Franklin Professor of Economics (emeritus)
University of Pennsylvania
3718 Locust Walk, Philadelphia, PA 19104-6297
Tel: 215 898 7713, Fax: 215 898 4477
E-mail:lrk@ssc.upenn.edu
and
Süleyman Özmucur
University of Pennsylvania
Department of Economics
3718 Locust Walk, Philadelphia, PA 19104-6297
Tel: 215 898 6765, Fax: 215 898 4477
E-mail:ozmucur@ssc.upenn.edu
Abstract
We present a perspective on the shape of the yield curve. We define, not one
particular relationship among interest rate and maturity, but an entire batch of
relationships between yield on the i-th treasury security and the set of multiple variables
that account for the movements over time of that yield. For each maturity, we find a
different set of explanatory variables. Our model for the yield curve is made up of as
many multivariate equations as there are major maturities that we are separately
considering. The performance of the model is compared with alternative models, such as
“no-change” and ARIMA using several criteria. The model performs significantly better
based on the mean absolute error, the mean square error, Theil inequality coefficient, and
Diebold-Mariano statistics. The model is also, in a statistical sense, significantly better in
predicting directional changes. A simple trading rule adopted also favors the model.
JEL Classification: C51, C52, C53, E43, E45
Keywords: interest rates, yield curve, forecasting, evaluation, estimation
∗
The authors are indebted to Joshua White, of Decision Economics, Inc., for insightful assistance on the
presentation of the material, especially for “real time” applications, and Giselle Guzman of Columbia
University for comments and suggestions.
Estimation of the US Treasury Yield Curve at
Daily and Intra-Daily Frequency
Lawrence R. Klein and
Süleyman Özmucur
In this era of gravitation by central banks towards inflation targeting, an
examination of its use as a major guide for macroeconomic policy and performance is
needed. The main policy instrument is the very short-term interest rate. In the United
States, this becomes the federal funds rate, which is an overnight rate for reconciling
required reserve balances among private banks.
The Federal Reserve and other central banks are quite accurate in hitting their
target values for the operative short-term rate, which is the federal funds rate in the
United States. For other countries different target rates are used, and there is no question
that central banks in the main advanced economies can hit their short-run targets with
great accuracy.
Control over the operative rate is, however, only the first step for implementation
of monetary policy. Economy-watchers attach great importance to the signals given off
by announcements of the targets for the operative rates, but do these rates serve well as
guides to the state of monetary policy – either in the direction of credit tightening, easing,
or staying put?
The entire yield curve and the entire span of interest rates are what really matter,
not to mention non-monetary policies, and our first step in this study is to examine how
good is the control over operative rates for interpreting the dynamics of the whole
spectrum of rates in any given economy.
2
The graph of some relevant time series of US interest rates from 1990 to early
2006 show the course of the federal funds rate, some closely allied treasury rates and a
medium-term treasury rate – the 10-year rate. After 1990 and the Gulf War period, the
Federal Reserve objective was to stimulate the macroeconomy by significantly lowering
the federal funds rate, but not much happened to the 10-year treasury rate, which is much
more relevant for judging or lowering private capital costs in order to know what to
expect in the form of economic stimulus.
Again, after 2001 and the Iraq War, the federal funds rate was the operative rate
and showed hardly any significant relationship to the 10-year treasury rate, either for the
downswing in the federal funds rate or for its upswing.
Eventually, large movements in the federal funds rate may percolate through to
the market sensitive rates for actual investment decisions, but the operative rate hardly
seems to be a reliable policy tool for influencing real economic activity.
It is evident in Figure 1, that some other short-term rates follow the federal funds
rate closely, but effective control over this operative rate does not lead to effective
control over the more meaningful rates that are used in basic investment decisionmaking, leading to capital formation.
3
Figure1. The Federal Funds Rate, and Yields on U.S. Treasury Securities
12
10
8
6
4
2
0
1990 1992 1994 1996 1998 2000 2002 2004
Federal Funds Rate Target
Average Effective Rate of Federal Funds
Yield on U.S. Treasury Securities (1-Month)
Yield on U.S. Treasury Securities (1-Year)
Yield on U.S. Treasury Securities (10-Year)
There are some important institutional reasons why there has been a weak
connection between the federal funds rate and a medium-term rate such as the 10-year
treasury rate, namely, that the technical environment for implementation of banking
operations has changed drastically in the information age, starting some time in the
1980s. When the federal funds rate was lowered along a steep gradient, plainly visible in
1991 and 1992, following the Gulf War, there was hardly any corresponding movement
4
in M2, because the meaning of money drastically changed in this period, and there was
little stimulus for borrowing in order to realize private investment goals.
US Macroeconomic Statistics, 1990-1993
GDP, % change
Unemployment, %
M2, %change
Federal Funds Rate, %
3-month treasury yield, %
10-year treasury yield, %
1990
1991
1992
1993
1.2
5.5
5.3
8.1
7.5
8.6
-0.6
6.7
3.2
5.7
5.4
7.9
2.3
7.4
2.1
3.5
3.4
7.0
3.1
6.8
1.3
3.0
3.0
5.9
________________________________________________________________
Source: OECD, Economic Survey, US, 1995
The graph of the federal funds rate and the 10-year treasury yield is highlighted
because the mortgage rate appears to follow this 10-year treasury rate and was
particularly important for the recent expansion of residential real estate investment which
sustained the overall economy significantly when many households paid very close
attention to their investment in real residential property, at a time when corporate
scandals turned many people away from trust in equity market or other security
investments.
Another aspect of the relation between the federal funds rate and the yield curve
in general, is that monetary authorities favor decisively the concept of inflation targeting.
A subtle change has taken place in the United States, in this respect.
5
It used to be that the Federal Reserve favored a broader statement about the goal
of monetary policy. One of their most important public affairs publications, The Federal
Reserve System, Purposes and Functions (1994) stated explicitly on p. 1, “Today, the
Federal Reserve’s Duties fall into four general areas: Conducting the nation’s monetary
policy by influencing the money and credit conditions in the economy in pursuit of full
employment and stable prices.”
This is only the first of four general areas of interest and responsibility, but it
differs from a more recent statement of the goals of monetary policy in the edition of
2005, which says (p.15), “Stable prices in the long run are a precondition for maximum
sustainable output growth and employment as well as moderate long-term interest rates.”
There is a very important and subtle distinction between the older and the new statement
of the goals of monetary policy.
Without declaring that they are formal inflation
targeters, it rationalizes their behavior in acting like other advanced industrial economies
that are more openly targeting inflation. The statement of 2005 makes price stability a
precondition, while in 1994 (p. 17) it states that “a stable level of prices appears to be the
condition most conducive to maximum sustained output.”
There is an admission that, “… in the short run some tension can exist between
the two goals”. [of sustainable output growth and employment at the same time as
achievement of price stability]”. It is our opinion that it is possible to generalize the
condition of the optimality region for more than one goal at a time.
The field of control theory is devoted to the optimization of weighted
combinations of multiple targets, subject to the constraint of dynamic movement of the
6
multivariate economy, accompanying an equation system of descriptive economic
performance. For inflation targeting, the focus is on the path of inflation alone, with
some informed attention paid to the other variables that would constitute a control
theorist’s loss or gain function.
In the United States, attention is directed towards the treasury yield curve, with
special emphasis on the ten-year rate at the present time, as well as the shape of the yield
curve.
The Meaning of the Yield Curve
The concept of the yield curve is a display of interest yields on various treasury
securities of different maturity. A normal yield curve begins with the overnight rate and
systematically spreads to rates of successive monthly maturity, to yearly maturities of
successive length, reaching up to the thirty-year treasury bond. The longer the maturity,
the higher the yield is the normal view. As maturity rises, there should be more risk,
requiring a higher yield, as long as the risk of repayment remains constant. For this
reason, the treasury yield curve is used because all treasury securities are viewed
presently as riskless; i.e. the US Treasury has not, in modern times, failed to pay interest
when due or principal at maturity.
It is a fact, however, that at various times the treasury yield curve becomes steeper
or less steep, and in the most embarrassing situation has inverted – by carrying a higher
yield on a short-term treasury than on some long-term treasuries.
Since the yield curve, at any time, might look like most other simplistic economic
relationships between two variables, interest level and maturity level, the yield curve
moves about, and a fixed relation between the ten-year treasury and the federal funds
7
rate, in Figure 1, does not show any simple relationship. In the graph, the federal funds
rate, monthly maturity rates (target and realized values) are all grouped together, showing
that maturities up to one year do, in fact, move closely with the federal funds rate,
making one solid “blur”, while the ten-year rate stands far apart, not at all showing a
tendency to move to where the Federal Reserve’s policy committee would like it to be.
There are significant stretches, where the federal funds rate is being moved down, to
stimulate the economy and the ten-year treasury rate hardly moves down by a comparable
magnitude.
Also there are protracted periods when the federal funds rate moves
significantly upwards, while the yield on the ten-year treasury hardly pays any attention
to the policy rate.
It is for this conceptual relation between yield and maturity, that we have an
entirely different perspective on the shape of the yield curve1. We define, not one
particular relationship between interest rate and maturity, but an entire batch of
relationships between yield on the i-th treasury security and the set of multiple variables
that account for the movements over time of that yield. For each maturity, we find a
different set of explanatory variables. There are systematic patterns, but not a simple
bivariate relationship between a particular yield and the corresponding security’s
maturity.
For us, every strategic point, for a given maturity on the yield curve is
determined by a different set of explanatory variables. Our yield curve is made up of as
many multivariate equations as there are major maturities that we are separately
1
There are many attempts to estimate the yield curve pioneered by McCulloch (1971,1975), and Nelson &
Siegel (1987). For alternative methods of estimation of the yield curve, see Boudoukh, Richardson, and
Whitelaw (2005), Carr, Halpern & McCallum (1974), Cochrane & Piazzesi (2002), Delbaen &Lorimier
(1992), Diebold & Li (2006), Diebold, Rudebusch, and Aruoba (2006), Evans (2005),Ioannides (2003),
Jordan (1982), Jordan & Mansi (2003), Linton, Mammen, Nielsen and Tanggaard (2001), Lustig, Sleet, and
8
considering.
For us, however, there are two key maturities, namely the overnight
maturity that constitutes the monetary authority’s operative rate and the ten-year treasury
because it appears to be so important for the mortgage market. The ten-year maturity
carries that significance now, but some other maturity may replace it as a focal point as
the economic situation evolves.
Our approach, thus, involves estimation of
(1) y it = f i ( x1t ...x nt ) + l it
y it = yield of the i-th treasury security at time t
x jt = j-th explanatory variable for estimating y it
l it = random error for estimating the yield of the i-th maturity.
Since some of the explanatory variables are outside the sphere of influence of
FED decisions; we emphasize that the FED does not control the yield curve or should not
even be convinced that it can estimate the yields on the various maturities by the methods
that it relies upon.
Our conception of the yield curve is presented in Figure 2 for days in the first five
months of 2006. The equations that determine points on this yield curve for a given day
are discussed in the next section, for each maturity.
The tendency for the yield curves, for different months of 2006, in Figure 2, to
drop from the 20-year to the 30-year treasury values; is not an inversion in the sense that
we are monitoring yields here, because the 30-year treasury was being phased out, but
then returned in this period.
Yeltekin (2005), McCulloch (1971, 1975), Nelson & Siegel (1987), Pham (1998), Piazzesi (2005), Shea
(1984, 1985), Siegel & Nelson (1988), and Wright (2006).
9
Figure 2
Yield Curves at Five Dates
in the Early Part of 2006
5.4
5.2
5.0
4.8
4.6
4.4
40
80 120 160 200 240 280 320 360
MATURITY (IN MONTHS)
JAN31
FEB28
MAR31
APR28
MAY12
The values of y it that determine the shape and position of the yield curve, at any
time point, t , must each be estimated from its corresponding function f i at time t.
Our objective in this paper is not only to estimate realistic yield curves for the US
economy, but also to attempt to do so in essentially real time i.e. we use variables in the
f i functions that are known in advance so that we can estimate yield curves every
10
working day and also at any time during that working day. We deal mainly with daily
market opening time and closing time for the US economy, but, in principle it can be
done for other economies and other time periods, no matter how close each time period is
to any other time period.
Estimates of the Daily Yield Curve Equations
We start with the (daily data) equation for the 1-month-treasury bill rate. All
variables preceded by D are in first difference form – today’s minus yesterday’s yield.
Also, all dependent variables are measured in daily differences2. The 1-month yield is
significantly related to the federal funds rate, the futures yield for a 2-year (the shortest
available futures) maturity, the “Monday” effect and an autoregressive error-moving
average transformation of first and second order residuals (Table 1, Appendix A)3.
We can say, of this estimate, that the degree of correlation is quite small and the
error term indicates absence of serial correlation. As for all the relevant yields of
securities and successive maturities, the explanatory variables must be known before the
market opens for daily trading in the USA.
The next equation, for a 3-month yield, has mainly the same specification, but the
degree of correlation is stronger and the autoregressive adjustments are for fourth and
tenth order.
2
The statistical package EViews 5.1 by the Quantitative Micro Software (QMS) is used in estimation of
equations. See QMS (2005).
3
Equations given here are the ones using final observations (May 12, 2006) available at the time of the
writing. In our experiments the ending period was May 11th for the prediction of yields on May 12th.
Similarly, ending period was January 20 for the prediction of the January 23rd yields. Chow prediction tests
indicate that there are no significant changes in coefficients of yield curve components during the January
23 through May 12 periods.
11
The equation for the 6-month yield has a similar specification, and continues to
follow the federal funds rate, as do the equations for the 1 and 3-month yields, and the
overall correlation continues to grow. An autoregressive estimate of third order is
significant.
The 1-year yield has a similar specification, but adds the Dow-Jones futures price,
and does not require an autoregressive or moving average transformation of error. The
overall correlation continues to grow.
The 2-year yield continues to show significant effect of the federal funds rate, but
the futures price in this equation is the 5-year value. The Monday effect is retained, as is
the Dow-Jones futures, but the euro deposit rate is added and the first 2 autoregressive
adjustments are used. The overall correlation continues to rise and there is no residual
serial correlation. The eurodollar deposit rate in all equations has a negative coefficient
when significant, suggesting a substitution relationship between US treasuries and euro
deposits.
The 3-year yield shows little relationship to the federal funds rate but is related to
the 2-year futures and the euro deposit rate, as well as the Dow Jones futures rate and also
the Monday effect. It has the same degree of correlation as the two year rate. Both the 1year and the 3-year rates do not appear to need correction for serially correlated
disturbances.
The 5-year yield equation moves up to higher overall correlation, but is not
significantly related to the federal funds rate. It is strongly related to its own futures
price. The euro deposit rate and the Dow-Jones futures, together with the Monday effect
round out the relationship. Two autocorrelation terms, AR (1) and AR (2) are significant.
12
The 7-year yield equation is negatively and insignificantly related to the federal
funds rate and negatively related to the euro deposit rate. It has significant positive
relationship with the expected inflation rate, the 10-year treasury futures rate, and the
Dow-Jones futures rate, and the Monday effect4.
The very important 10-year equation has several significant variables, apart from
the constant term. It is negatively associated with the Federal Funds Rate and the euro
deposit rate, inflation expectations, the 10-year futures rate, the Dow-Jones futures, the
Monday effect, and an autoregressive correction factor. The 20-year equation is the first
in serial order to show an overall correlation in excess of 0.93. It shows a significant
negative relationship to the federal funds rate, and the euro interest rate.
Inflation
expectations, the 30-year futures rate, and the Dow-Jones futures rate have positive
effects. It is not significantly related to the euro deposit rate.
The 30-year bond was withheld from the market when the Clinton Administration
was realizing large budget surpluses. The futures yield for the newly introduced treasury
bond future is significant, but the euro deposit rate is not. The expected inflation rate
shows a significant positive effect and the federal funds rate a negative effect. A first
order autoregressive error correction term is significant.
Each of these displayed equations provides an estimate for one point at a given
time period on our yield curve, on the basis of known explanatory variables at the start of
each day’s trading. At the beginning of each trading day, during the day, and at closing,
4
The expected inflation rate is measured as the spread between the unprotected yield on 10-year treasuries
and inflation protected 10-year treasuries (TIPS). High demand for protection would tend to drive down the
yield on TIPS and increase the spread; while monetary authorities try to raise the whole yield curve, by talk
and action. With a time lag, some positive effect can be expected.
13
our system can estimate the whole yield curve, according to our conception of it. Yield
curves for each of five separate days are shown in Figure 2, above.
Table 1. A Summary of Estimated Treasury Yield Equations
1-month
3-month
1-year
6-month
CONSTANT
0.004
*
-0.005
*
-0.004
*
-0.003
D(FEDERAL FUNDS
RATE)
*
0.108
**
0.089
**
0.092
*
0.036
***
D(TREASURY FUTURES (2
YEAR))
0.090
*
0.226
*
0.351
*
0.562
*
D(TREASURY FUTURES (5
YEAR))
2-year
3-year
-0.001
-0.001
0.049
**
0.002
0.855
0.812
*
-0.002
**
-0.002
*
D(TREASURY FUTURES
(10-YEAR))
D(TREASURY FUTURES
(30-YEAR))
D(EXPECTED INFLATION
(T-1))
D(EXPECTED
EURODOLLAR DEPOSIT
RATE )
DLOG(DOW-JONES
FUTURES)*100
MONDAY
-0.016
*
0.027
*
0.023
*
DUMMY911
-0.198
*
-0.110
*
-0.088
**
***
0.001
**
0.003
*
0.003
*
0.014
*
0.005
*
0.003
***
0.749
*
DUMMY30
AR(1)
0.618
*
-0.075
***
AR(2)
-0.999
*
-0.061
***
AR(3)
AR(4)
0.041
***
AR(10)
0.128
*
0.193
*
MA(1)
-0.610
*
MA(2)
0.983
*
Adjusted R2
0.199
*
Durbin-Watson
1.831
2.023
-0.095
**
0.392
*
1.980
0.612
*
2.061
______________________________________________________________________________________
(*) Significant at the one percent level
(**) Significant at the five percent level
(***) Significant at the ten percent level
14
0.759
2.001
*
2.147
Table 1. A Summary of Estimated Treasury Yield Equations (continued)
CONSTANT
5-year
7-year
10year
20year
30year
-0.001
0.000
-0.001
0.000
0.000
0.019
-0.007
-0.019
**
1.013
*
D(FEDERAL FUNDS
RATE)
-0.017
*
-0.018
**
0.989
*
0.888
*
**
0.032
*
D(TREASURY FUTURES (2
YEAR))
D(TREASURY FUTURES (5
YEAR))
0.908
*
D(TREASURY FUTURES
(10-YEAR))
1.082
*
D(TREASURY FUTURES
(30-YEAR))
D(EXPECTED INFLATION
(T-1))
D(EXPECTED
EURODOLLAR DEPOSIT
RATE )
-0.002
***
0.023
**
0.042
*
0.015
-0.002
**
-0.002
**
-0.001
0.001
*
0.000
DLOG(DOW-JONES
FUTURES)*100
0.003
*
0.002
*
0.003
*
MONDAY
0.004
*
0.002
**
0.004
*
-0.059
*
AR(1)
-0.147
*
-0.075
**
-0.161
*
-0.191
*
AR(2)
-0.067
*
Adjusted R2
0.841
*
0.866
*
0.933
*
0.819
*
Durbin-Watson
2.001
DUMMY911
DUMMY30
AR(3)
AR(4)
AR(10)
MA(1)
MA(2)
0.880
2.226
*
2.000
2.028
______________________________________________________________________________________
(*) Significant at the one percent level
(**) Significant at the five percent level
(***) Significant at the ten percent level
15
2.037
A Forecast Error Experiment
For every trading day in the interval January 23, 2006 through May 12, 2006, we
tested the forecast power of our system for 11 maturities (1 mo., 3 mos., 6 mos., 1 yr., 2
yrs., 3 yrs., 5 yrs., 7 yrs., 10 yrs.,. 20 yrs., 30 yrs.). Average absolute and root mean
square errors for closing yields were tabulated daily.
At all maturities, our yield
estimates had smaller average errors than those of simplistic models.
simplistic model 1: no daily change; today’s yield = yesterday’s yield (myopic
expectations)
simplistic model 2: ARIMA equations (autoregressive, i.e. ARIMA(p,1,0))
For all maturities, from 1 month to 30 years, those that were studied performed better
than simplistic models, in the sense that average absolute or root mean square error was
systematically lower in our model. In particular, the much-studied and popular 10-year
treasury yield was consistently (but not for every day) estimated with about 2 basis points
lower error than in the simplistic mechanical or autoregressive models.
We have tried to model the effects of advance indicators that are known prior to
trading on each market day. Apart from the finding that we have realized, on average, a
smaller absolute error, measured in basis points, by using our model equations in this
empirical test, we encountered some market features that are worth pointing out.
At the present time (early days of 2006) we found that using a reading of crude oil
price and gold price, both featured as contributing to external inflationary shocks, made
our equations perform more poorly.
We have no satisfactory explanation for the
“Monday” effect, but it does seem to have some empirical bearing on the market for US
treasury securities.
16
Table 2. Mean Absolute Error and Root Mean Square Error (basis points) (1/23/06-5/12/06)
Mean Absolute Error (basis points)
1-month
3-month
6-month
1-year
2-year
3-year
5-year
7-year
10-year
20-year
30-year
Model
2.30
1.49
1.36
1.26
1.36
1.13
1.19
1.03
1.03
1.17
1.28
Mechanical
2.61
1.60
2.00
2.32
3.10
2.89
3.39
3.15
3.07
3.46
3.21
ARIMA
2.64
1.63
2.10
2.39
3.15
2.92
3.42
3.19
3.11
3.48
3.22
Model minus
Mechanical
-0.31
-0.11
-0.64
-1.06
-1.74
-1.76
-2.20
-2.12
-2.04
-2.29
-1.93
Model
minus
ARIMA
-0.34
-0.13
-0.74
-1.13
-1.79
-1.79
-2.23
-2.16
-2.07
-2.32
-1.94
Root Mean Square Error (basis points)
Model
Mechanical
ARIMA
Model
minus
ARIMA
Model minus
Mechanical
1-month
3.95
4.51
4.40
-0.56
-0.45
3-month
1.97
2.02
2.10
-0.06
-0.13
6-month
2.02
2.85
2.87
-0.83
-0.86
1-year
1.92
3.13
3.20
-1.21
-1.28
2-year
2.10
4.08
4.12
-1.98
-2.03
3-year
1.48
3.80
3.80
-2.32
-2.32
5-year
2.51
4.80
4.86
-2.28
-2.34
7-year
1.47
4.03
4.08
-2.57
-2.61
10-year
1.29
3.79
3.83
-2.50
-2.54
20-year
2.68
4.55
4.63
-1.87
-1.95
30-year
1.84
4.10
4.07
-2.26
-2.23
Some major events took place during our test period. The 30-year treasury bond
had been retired as a result of redemption policy initiated by the US Treasury when the
government’s fiscal policy produced surpluses instead of deficits – an unusual situation.
The financial community protested the absence of a good long-term measuring
instrument for inflation, and eventually the 30-year bond was re-issued during the period
17
of our test. That event re-directed activity away from our equations, for a few days, and
the observed errors were larger, but corrected in a short time span of a few days.
The transfer of chairmanship at the Federal Reserve took place during our test
period, and this also brought about market re-direction for a short period of days.
Although gold and oil price changes did not improve the forecasting performance
of our equations, they did appear to have monetary influence from time to time. We
direct the readers’ attention to our table of errors (Appendix B) for the following dates:
February 1, 8, 10 and March 9, 16, 28 for the yield forecasts of the 10-year note. For the
20-year treasury, February 1, 2, 3 were bad days for yield forecasts. The 30-year bond
forecast errors were quite low on February 1, 2, 3, 15, 16 but large on February 9, 10.
The long bonds (30-year) had low errors March 17, 20, 21, 22, 23.
Equations were estimated every morning, before 8am, and forecasts for the end of
the day rates were obtained. At the end of the day, these were compared with actual
figures. These are given in Appendix B. In order to check forecasting ability of the
model, various statistics were used, and comparisons with alternative models were made5.
Comparisons for the January 23-May 12 period (80 observations) are given in
Table 2. Mean absolute error and root mean square error based on 80 periods indicate that
our model performs better than alternative models (no change, and ARIMA)6. Mean
absolute error for the 1-month rate is 2.3 basis points. Errors are much smaller for other
maturities. For example, average absolute error is 1.03 basis points for the 10-year and 75
For forecast evaluation see Clements (2005), Clements & Hendry (1998, 2002). Diebold (2004), Granger
& Newbold (1973, 1986), Klein (2000), Klein & Young (1980), Mariano (2002), Theil (1961), and Tsay
(2005).
6
ARIMA (p, d , q) models are identified and estimated using the Box-Jenkins (1976) methodology. See,
also Hamilton (1994) and Tsay (2005). Orders are different for different maturities. For example, ARIMA
18
year, and 1.26 basis points for the 1-year treasury securities. These errors are much
smaller than errors in the alternative models. For example, average absolute error for the
10-year rate is 3.07 basis points for the mechanical model (no change) and 3.11 basis
points for the ARIMA (3,1,0) model. Root mean square errors are also smaller for our
model. For example, root mean square error for the 10-year treasury is 1.29 basis points.
Corresponding figures are 3.79 for the “no change” model and 3.83 for the ARIMA.
These are significant differences.
The graphs (Figures 3, 4, 5, 6) show relationships between actual daily yields and
predictions of yields, one day ahead. Figure 3 plots actual daily values and predicted
daily values, over the time span of our experimental calculations. Figures 4 and 5 plot
predicted (ordinate) versus realized (abscissa) values, over the time span of our
experiment. Perfect prediction should lie along a straight line (45 degrees). The scatters
of plotted points show low dispersion as maturity lengthens. It is generally the case that
change-values of predictions and realizations are less closely correlated, and again the
degree of correlation rises with the length of maturity. Estimated yield curves for selected
dates (end-of-month or data period) indicate that they are very close to actual curves,
which are available at the end of the day (Figure 6).
The forecasting accuracy of the model can be seen by the correlation between
actual and predicted values and the Theil inequality coefficient. Correlations between
actual and ex-ante forecast lie between 0.97 for the 1-month rate and 0.998 for the 10year rate (Table 3, Figure 3). Theil Inequality coefficients are very close to zero,
indicating a close fit (Table 3). The decomposition of the inequality coefficient can be
(7, 1, 0) is used for the 1-month rate, and ARIMA (3, 1, 0) is used for the 10-year rate. These are available
from the authors.
19
very useful to see the source of the error. The bias proportion is very small, less than 0.03
for the 1-month rate and less than 0.045 for the 10-year rate. On the other hand,
covariance proportion is above 0.90 for the 1-month rate, and above 0.93 for the 10-year
rate. Prediction and realization diagrams lie very close to a 45 degree line (perfect fit)
(Figure 4).
Table 3. Theil Inequality Coefficient
1-month
3-month
6-month
1-year
2-year
3-year
5-year
7-year
10-year
20-year
30-year
Theil
Inequality
coefficient
0.0044
0.0021
0.0021
0.002
0.0022
0.0016
0.0026
0.0015
0.0013
0.0027
0.0019
bias
proportion
0.028
0.0236
0.04
0.0181
0.0019
0.0332
0.0088
0.0129
0.0424
0.0107
0.0544
variance
proportion
0.0697
0.013
0.0148
0.0003
0.0003
0.0033
0.0066
0.0023
0.0213
0.0038
0.0126
covariance
proportion
0.9024
0.9634
0.9452
0.9816
0.9977
0.9635
0.9846
0.9848
0.9363
0.9856
0.933
0.971
significance
of the
correlation
coefficient
*
0.534
significance
of the
correlation
coefficient
*
0.987
*
0.389
*
0.989
*
0.71
*
0.99
*
0.81
*
0.99
*
0.876
*
0.996
*
0.946
*
0.991
*
0.881
*
0.997
*
0.938
*
0.998
*
0.951
*
0.994
*
0.812
*
0.997
*
0.919
*
Correlation
(actual &
forecasts)
Correlation
(change in
actual &
forecasts)
(*) Significant at the one percent level.
It is possible to test if these errors, which are smaller for the model, are
statistically significant. This can be done with the use of a Diebold-Mariano statistic.
There are several advantages of the Diebold-Mariano statistic. Forecast errors do not
have to be equal to zero, and they do not have to be normally distributed. Furthermore, it
is also very flexible; the researcher is able to determine the loss function. The statistic
has an asymptotic normal distribution7. Diebold-Mariano statistics based on 80 forecast
periods with a rectangular kernel and five lags are given in Table 4. Both loss functions,
square of forecast errors and absolute value of forecast errors, yield the same conclusion.
7
See Diebold & Mariano (1995). There are small sample modifications of this asymptotic statistic. For a
survey, see Mariano (2002), and Clements (2005).
20
In these tests the model is compared with the “no change” model8. The model has
significantly smaller errors than alternative models at the one percent level for all
maturities, except 1-month and 3-month. The model has smaller errors (negative figures)
for the 1-month and 3-month rates, but not statistically significant at the five percent
level.
Table 4. Diebold-Mariano Statistics with Alternative Loss Functions
1-month
3-month
6-month
1-year
2-year
3-year
5-year
7-year
10-year
20-year
30-year
Loss
Function:
Square of
forecast
errors
-1.85
-0.6
-3.46
-3.03
-3.82
-4.51
-2.78
-5.41
-8.05
-3.65
-24.61
Significance
***
*
*
*
*
*
*
*
*
*
Loss
Function:
Absolute
value of
Forecast
Errors
-1.85
-0.47
-2.79
-4.09
-6.18
-7.74
-5.4
-7.05
-10.42
-11.24
-10.89
Significance
***
*
*
*
*
*
*
*
*
*
(*) Significant at the one percent level.
(***) Significant at the ten percent level.
Another criterion to evaluate the performance of the model is the ability to predict
directional change (here, daily changes in treasury yields). This can be done by
comparing actual change from a day earlier (At-At-1) with the predicted change (Pt-At-1),
where P is the predicted, and A is the actual yield. If both changes are positive or
negative, it is a correct prediction of the change. If the actual change is positive, but the
predicted change is negative, or the actual change is negative and the predicted change is
positive, it is an error in prediction of the change (Table 5, Appendix B). Prediction8
Similar results are obtained for comparisons with ARIMA models.
21
realization diagrams on changes (Figure 5) are also close to a 45 degree line, except for
treasuries with shorter maturities. These can be seen in lower correlations between
changes in actual and predicted values (Table 3). For example, the correlation between
changes in actual and changes in predicted 10-year rate is 0.95, but the correlation is only
0.39 for the 3-month rate. There are 45 cases where there is an increase in the yield and
the directional prediction of the yield is an increase (correct prediction) in the 10-year
treasuries (Table 5). In one case, the model prediction is an “increase”, but the actual
change is a “decrease” (incorrect prediction). In five cases, the model prediction is a
“decrease”, but the actual change is an “increase” (incorrect prediction). There are 29
cases where there is a decrease in the yield and the directional prediction of the yield is
also a decrease (correct prediction). There are 74 correct (93%) and 6 incorrect
predictions out of a total of 80 daily changes in the 10-year yield. The model performs
slightly better when rates are decreasing than when they are increasing. For example, the
percent of correct prediction in the 10-year yield is 90% (45/(45+5)*100) when rates are
increasing (actual change is positive) and 97% (29/(29+1)*100) when rates are
decreasing (actual change is negative). The chi-square (χ2) test for the 10-year yield
(Tsay, 2005) indicates that the model outperforms a random choice model with equal
probabilities of upward and downward movements. The model performs very well in
terms of prediction of changes with treasury yields of maturities from 1-year through 20year. About 90 percent of changes are predicted correctly. The performance is relatively
good for the 6-month (79%) and 30-year (83%) maturities. The accuracy of predicting
changes are not that good for treasuries with 1-month and 3-month maturities. Based on
22
directional measure of χ2 tests the model does significantly better, with the exception of
the 3-month yield.
Table 5. Prediction of Turning Points (80 daily changes)
1-month
3-month
6-month
1-year
2-year
3-year
5-year
7-year
10-year
20-year
30-year
Predi
ction
up
and
actual
up
Predicti
on up
and
actual
down
Predicti
on
down
and
actual
up
Predicti
on
down
and
actual
down
Number
of
correct
predicti
ons
(1)
35
37
45
50
49
51
49
47
45
45
40
Numb
er of
incorr
ect
predic
tions
share of
correct
predicti
ons
(actualup)
share of
correct
predicti
ons
(actualdown)
(2)
(3)
(4)
(1+4)
(2+3)
1/(1+3)
4/(2+4)
11
9
3
2
1
3
1
0
1
2
2
12
23
14
6
7
6
6
8
5
8
12
22
11
18
22
23
20
24
25
29
25
26
57
48
63
72
72
71
73
72
74
70
66
23
32
17
8
8
9
7
8
6
10
14
0.74
0.62
0.76
0.89
0.88
0.89
0.89
0.85
0.90
0.85
0.77
0.67
0.55
0.86
0.92
0.96
0.87
0.96
1.00
0.97
0.93
0.93
share of
total
correct
predicti
ons
(1+4)/(1
+2+3+4
)
0.71
0.60
0.79
0.90
0.90
0.89
0.91
0.90
0.93
0.88
0.83
(*) Significant at the one percent level.
A Trading Experiment
It is possible to have a simple experiment of daily transactions to see the
performance of the model in a trading setting. For this experiment it may be better to
work with prices, which are calculated as 100 minus the yield. A simple decision rule
which is exercised at the beginning of the day, and the gain or loss at the end of the day is
easily seen. The same experiment is repeated for all the days to compare the performance
of the model against the mechanical model.
23
Signif
icance
Chisquare
(χ2)
13.4
1.7
24.8
48.4
49.8
43.6
53.1
51.8
57.6
44.3
35.5
*
*
*
*
*
*
*
*
*
*
The simple rule involves comparison of actual price (A) at the beginning of the
day and its predicted value (P) at the end of the day. If predicted change in the price is
positive, i.e. Pt – At-1 >0, then the suggested decision is to “buy”. The gain, which may
turn out to be negative also, at the end of the day is Gt = A t – A t-1. If the prediction is
correct, there will be a positive gain. If predicted change in the price is negative, i.e. Pt – At-1
<0, then the suggested decision is to “sell”. The gain (or loss avoided) at the end of the
day is Gt = A t-1 – A t, or Gt = (-1)*(A t – A t-1). If the prediction is correct, there will be a gain
since the price at the end of the day is lower than the price at the beginning of the day. The sum
of these daily gains indicates a higher return for the model (Table 6). For example, for the 10-year
treasuries, the sum of gains in 80 days is 2.42, compared to a gain of 0.82 for the mechanical
model9. If the trading cost is 8 cents per $100 par value10, the net gain for $1,000 in 80 days is
$1,356 (2.42*1000-80*(0.08/100)*1000-1000) with a percentage return of 135.6%, compared to
a loss of $244 (negative 24.4% return) in the mechanical model. The returns are even higher for
5-year (160.6%) and 7-year (139.6%) treasuries. Results for other treasuries are also very
favorable, with the exception of the 3-month treasuries. The un-weighted average return is 93.7%
for the model, and negative 37.2% for the mechanical model.
9
The cost of transaction and other fees are not considered in these calculations. This is really not an issue
in comparisons with the mechanical model, because same costs apply to every case.
10
The bid-ask spread figure of 8 cents per $100 par value is obtained from Chakravarty & Sarkar (2001).
However, any other possible costs accrued do not change the major conclusion that the model performs
better than the mechanical model. It should be noted that for individual investors trading directly at the
Treasury web-site, there is a $45 “penalty” for selling before maturity. See U.S. Treasury (2006).
24
Table 6. Performance in Daily Trading
Gain
Model
Mechanical
Difference
Net Gain ($1000 value, 8cent/$100
cost per transaction)
Percent Net Gain
Model
Mechanical
Difference
Model
-374
900
52.6
Mechanical
-37.4
Difference
1-month
1.59
0.69
0.90
526
3-month
0.44
0.50
-0.06
-624
-564
-60
-62.4
-56.4
-6.0
6-month
1.44
0.52
0.92
376
-544
920
37.6
-54.4
92.0
1-year
1.80
0.56
1.24
736
-504
1240
73.6
-50.4
124.0
2-year
2.34
0.64
1.70
1276
-424
1700
127.6
-42.4
170.0
3-year
2.21
0.71
1.50
1146
-354
1500
114.6
-35.4
150.0
5-year
2.67
0.77
1.90
1606
-294
1900
160.6
-29.4
190.0
7-year
2.46
0.80
1.66
1396
-264
1660
139.6
-26.4
166.0
10-year
2.42
0.82
1.60
1356
-244
1600
135.6
-24.4
160.0
20-year
2.41
0.85
1.56
1346
-214
1560
134.6
-21.4
156.0
30-year
2.23
0.75
1.48
1166
-314
1480
116.6
-31.4
148.0
22.01
7.61
14.40
10306
-4094
14400
93.7
-37.2
130.9
Total
90.0
Conclusion
A model which is used to estimate points on the yield curve by forecasting
treasury yields at different maturities using different explanatory variables is constructed.
Once the final structure was established, the eleven-equation model was re-estimated
every morning to forecast the end of the day treasury yields. The performance of the
model is compared with alternative models, such as “no-change” and ARIMA using
several criteria. The model performs significantly better based on the mean absolute
error, the mean square error, Theil inequality coefficient, and Diebold-Mariano statistics.
The model is also better, in a statistically significant sense, in predicting directional
changes. A simple trading rule adopted also favors the model in all cases, with the
exception of the 3-month treasury yield. In general, the performance of the model
improves with maturity; the performance is much better for yields of longer maturities.
25
Figure3. Actual and Ex-ante Forecasts
4.8
5.0
4.7
4.9
4.6
4.8
4.5
4.4
4.7
4.3
4.6
4.2
4.5
4.1
4.0
r=0.971, MAE=2.30, RMSE=3.95, U=0.0044
4.4
R=0.987, MAE=1.49, RMSE=1.97, U=0.0021
4.3
3.9
2006:02
2006:03
Actual_1-month
2006:04
2006:02
Forecast_1-month
Actual_3-month
5.1
5.1
5.0
5.0
4.9
4.9
4.8
4.8
4.7
4.7
4.6
4.6
4.5
2006:03
4.5
2006:04
Forecast_3-month
r=0.990, MAE=1.26,RMSE=1.92,U=0.0020
r=0.989,MAE=1.36,RMSE=2.02,U=0.0021
4.4
4.4
2006:02
2006:03
Actual_6-month
2006:04
2006:02
Forecast_6-month
2006:03
Actual_1-year
26
2006:04
Forecast_1-year
Figure3. Actual and Ex-ante Forecasts (Continued)
5.1
5.1
5.0
5.0
4.9
4.9
4.8
4.8
4.7
4.7
4.6
4.6
4.5
4.5
r=0.990, MAE=1.36,RMSE=2.10, U=0.0022
4.4
4.3
4.4
r=0.996, MAE=1.13, RMSE=1.48, U=0.0016
4.3
2006:02
2006:03
Actual_2-year
2006:04
2006:02
Forecast_2-year
5.1
5.2
5.0
5.1
4.9
5.0
4.8
4.9
4.7
4.8
4.6
4.7
4.5
4.6
4.4
4.5
4.3
r=0.991, MAE=1.19, RMSE=2.51, U=0.0026
4.2
2006:03
Actual_3-year
4.4
2006:04
Forecast_3-year
r=0.997, MAE=1.03,RMSE=1.47,U=0.0015
4.3
2006:02
2006:03
Actual_5-year
2006:04
2006:02
Forecast_5-year
2006:03
Actual_7-year
27
2006:04
Forecast_7-year
Figure3. Actual and Ex-ante Forecasts (Continued)
5.2
5.6
5.1
5.4
5.0
4.9
5.2
4.8
5.0
4.7
4.6
4.8
4.5
4.6
4.4
r=0.998, MAE=1.03,RMSE=1.29, U=0.0013
r=0.994, MAE=1.17,RMSE=2.68, U=0.0027
4.4
4.3
2006:02
2006:03
Actual_10-year
2006:04
2006:02
Forecast_10-year
5.3
5.2
5.1
5.0
4.9
4.8
4.7
4.6
4.5
r=0.997, MAE=1.28, RMSE=1.84, U=0.0019
4.4
2006:02
2006:03
Actual_30-year
2006:03
Actual_20-year
2006:04
Forecast_30-year
28
2006:04
Forecast_20-year
Figure 4. Prediction and Realization Diagrams
4.8
4.9
4.7
4.8
Forecast_3-month
Actual_1-month
4.6
4.5
4.4
4.3
4.2
4.1
4.7
4.6
4.5
4.4
4.0
3.9
3.9 4.0 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8
4.3
4.3
4.4
5.1
5.1
5.0
5.0
4.9
4.9
4.8
4.7
4.6
4.5
4.4
4.4
4.5
4.6
4.7
4.8
4.9
5.0
5.0
5.1
Actual_3-month
Actual_1-year
Actual_6-month
Forecast_1-month
4.8
4.7
4.6
4.5
4.5
4.6
4.7
4.8
4.9
5.0
5.1
4.4
4.4
Forecast_6-month
4.5
4.6
4.7
4.8
4.9
Forecast_1-year
29
5.1
5.1
5.0
5.0
4.9
4.9
Actual_3-year
Actual_2-year
Figure 4. Prediction and Realization Diagrams (Continued)
4.8
4.7
4.6
4.8
4.7
4.6
4.5
4.5
4.4
4.4
4.3
4.3 4.4 4.5 4.6 4.7 4.8 4.9 5.0 5.1
4.3
4.3 4.4 4.5 4.6 4.7 4.8 4.9 5.0 5.1
Forecast_3-year
5.1
5.2
5.0
5.1
4.9
5.0
4.8
4.9
Actual_7-year
Actual_5-year
Forecast_2-year
4.7
4.6
4.5
4.8
4.7
4.6
4.4
4.5
4.3
4.4
4.2
4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5.0 5.1
4.3
4.3 4.4 4.5 4.6 4.7 4.8 4.9 5.0 5.1 5.2
Forecast_5-year
Forecast_7-year
30
Figure 4. Prediction and Realization Diagrams (Continued)
5.2
5.6
5.1
5.4
4.9
Actual_20-year
Actual_10-year
5.0
4.8
4.7
4.6
4.5
5.0
4.8
4.6
4.4
4.4
4.4
4.3
4.3 4.4 4.5 4.6 4.7 4.8 4.9 5.0 5.1 5.2
Forecast_10-year
4.6
4.8
5.0
5.2
Forecast_20-year
5.3
5.2
5.1
Actual_30-year
5.2
5.0
4.9
4.8
4.7
4.6
4.5
4.4
4.4 4.5 4.6 4.7 4.8 4.9 5.0 5.1 5.2 5.3
Forecast_30-year
31
5.4
5.6
Figure 5. Prediction and Realization Diagrams (Changes in Actual and Forecasts)
CHANGE(Actual_1-month)
.25
r=0.534
.30
.06
.25
.04
.20
.20
.15
.15
.10
.10
.05
.05
.00
.00
-.05
-.05
CHANGE(Forecast_3-month)
.30
r=0.389
.02
.00
-.02
-.04
-.06
-.08
-.02
-.10
-.10
-.03 -.02 -.01 .00 .01 .02 .03 .04 .05 .06
CHANGE(Forecast_1-month)
.08
.08
.01
.02
.03
.04
r=0.810
.06
CHANGE(Actual_1-year)
.06
CHANGE(Actual_6-month)
.00
CHANGE(Actual_3-month)
r=0.710
.04
.02
.00
-.02
-.04
-.06
-.04
-.01
.04
.02
.00
-.02
-.04
-.02
.00
.02
.04
.06
-.06
-.08
.08
CHANGE(Forecast_6-month)
-.04
.00
.04
.08
CHANGE(Forecast_1-year)
32
.12
Figure 5. Prediction and Realization Diagrams (Changes in Actual and Forecasts)
(Continued)
.10
.12
r=0.876
r=0.946
CHANGE(Actual_3-year)
CHANGE(Actual_2-year)
.08
.05
.00
-.05
-.10
-.08
-.04
.00
.04
.08
.04
.00
-.04
-.08
-.12
-.08 -.06 -.04 -.02 .00 .02 .04 .06 .08
.12
CHANGE(Forecast_2-year)
.12
r=0.881
.08
CHANGE(Actual_7-year)
CHANGE(Actual_5-year)
.12
CHANGE(Forecast_3-year)
.04
.00
-.04
-.08
-.12
-.12 -.08 -.04 .00
.04
.08
.12
.16
r=0.938
.08
.04
.00
-.04
-.08
-.12
-.08
CHANGE(Forecast_5-year)
-.04
.00
.04
.08
CHANGE(Forecast_7-year)
33
.12
Figure 5. Prediction and Realization Diagrams (Changes in Actual and Forecasts)
(Continued)
.12
r=0.951
CHANGE(Actual_20-year)
CHANGE(Actual_10-year)
.10
.05
.00
-.05
CHANGE(Forecast_10-year)
CHANGE(Actual_30-year)
r=0.919
.00
-.05
-.10
-.15
-.08
-.04
.00
.04
.04
.00
-.04
-.12
-.08
-.04
.00
.04
CHANGE(Forecast_20-year)
.05
-.20
-.12
.08
-.08
-.16
-.10
-.08 -.06 -.04 -.02 .00 .02 .04 .06 .08
.10
r=0.812
.08
CHANGE(Forecast_30-year)
34
.08
Figure 6. Actual and Estimated Yield Curves for Selected Dates
4.7
4.70
4.6
4.65
4.5
4.60
4.4
4.55
4.3
4.50
40
80
120
160
200
240
280
320
360
40
80
120
MATURITY
160
200
240
280
320
360
320
360
MATURITY
ACTUAL_JAN31
JAN31
ACTUAL_FEB28
FEB28
5.3
5.0
5.2
5.1
4.9
5.0
4.9
4.8
4.8
4.7
4.7
4.6
40
80
120
160
200
240
280
320
360
40
MATURITY
MAR31
5.3
5.2
5.1
5.0
4.9
4.8
4.7
120
160
200
240
280
320
360
MATURITY
ACTUAL_MAY12
160
200
ACTUAL_APR28
5.4
80
120
240
280
MATURITY
ACTUAL_MAR31
40
80
MAY12
35
APR28
References
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Pham, Toan M. (1998). “Estimation of the Term Structure of Interest Rates: An
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www.federalreserve.gov
38
APPENDIX A: ESTIMATED EQUATIONS
Dependent Variable: D(YIELD ON TREASURY SECURITIES (1-MONTH))
Method: Least Squares
Sample (adjusted): 8/03/2001 5/12/2006
Included observations: 1246 after adjustments
Convergence achieved after 16 iterations
Newey-West HAC Standard Errors & Covariance (lag truncation=6)
Backcast: 8/01/2001 8/02/2001
Variable
Coefficient
Std. Error
t-Statistic
Prob.
0.0044
0.1076
0.0900
-0.0164
-0.1983
0.6178
-0.9988
-0.6100
0.9826
0.0015
0.0474
0.0173
0.0031
0.0527
0.0014
0.0012
0.0063
0.0073
2.9961
2.2681
5.2069
-5.3689
-3.7664
436.3722
-811.3225
-96.4740
134.3092
0.0028
0.0235
0.0000
0.0000
0.0002
0.0000
0.0000
0.0000
0.0000
0.0008
0.0444
-3.6074
-3.5704
39.6
0.0000
CONSTANT
D(FEDERAL FUNDS RATE)
D(TREASURY FUTURES (2 YEAR))
MONDAY
DUMMY911
AR(1)
AR(2)
MA(1)
MA(2)
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
Durbin-Watson stat
0.2040
0.1989
0.0397
1.9502
2256.4
1.8306
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
F-statistic
Prob(F-statistic)
Inverted AR Roots
Inverted MA Roots
.31+.95i
.30-.94i
.31-.95i
.30+.94i
Chow Forecast Test: Forecast from 1/23/2006 to 5/12/2006
F-statistic
Log likelihood ratio
1.002181
83.48169
Prob. F(80,1157)
Prob. Chi-Square(80)
39
0.475760
0.373005
Dependent Variable: D(YIELD ON TREASURY SECURITIES ( 3-MONTH))
Method: Least Squares
Sample: 1/01/1997 5/12/2006
Included observations: 2443
Convergence achieved after 6 iterations
Newey-West HAC Standard Errors & Covariance (lag truncation=8)
Variable
Coefficient
Std. Error
t-Statistic
-0.0052
0.0886
0.2258
0.0267
-0.1098
0.0408
0.1283
0.0010
0.0349
0.0243
0.0027
0.0394
0.0254
0.0314
-5.2323
2.5387
9.2993
9.9654
-2.7868
1.6035
4.0896
0.0000
0.0112
0.0000
0.0000
0.0054
0.1090
0.0000
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
F-statistic
Prob(F-statistic)
-0.0001
0.0460
-3.5316
-3.5149
98.5
0.0000
CONSTANT
D(FEDERAL FUNDS RATE)
D(TREASURY FUTURES (2 YEAR))
MONDAY
DUMMY911
AR(4)
AR(10)
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
Durbin-Watson stat
0.1952
0.1933
0.0413
4.1612
4320.8
2.0233
Inverted AR Roots
.82
.22-.77i
-.64+.44i
.64-.44i
.22+.77i
.64+.44i
.22+.77i
-.22-.77i
-.82
-.64-.44i
Chow Forecast Test: Forecast from 1/23/2006 to 5/12/2006
F-statistic
Log likelihood ratio
0.206650
17.08281
Prob. F(80,2356)
Prob. Chi-Square(80)
40
Prob.
1.000000
1.000000
Dependent Variable: D(YIELD ON TREASURY SECURITIES (6-MONTH))
Method: Least Squares
Sample: 1/01/1997 5/12/2006
Included observations: 2443
Convergence achieved after 5 iterations
Newey-West HAC Standard Errors & Covariance (lag truncation=8)
Variable
Coefficient
Std. Error
t-Statistic
Prob.
-0.0045
0.0919
0.3514
0.0232
-0.0876
-0.0950
0.0007
0.0280
0.0236
0.0017
0.0360
0.0423
-6.7340
3.2841
14.9139
13.3725
-2.4339
-2.2455
0.0000
0.0010
0.0000
0.0000
0.0150
0.0248
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
F-statistic
Prob(F-statistic)
-0.0001
0.0395
-4.1190
-4.1047
315.8
0.0000
CONSTANT
D(FEDERAL FUNDS RATE)
D(TREASURY FUTURES (2 YEAR))
MONDAY
DUMMY911
AR(3)
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
Durbin-Watson stat
0.3932
0.3919
0.0308
2.3145
5037.3
1.9800
Inverted AR Roots
.21+.36i
.21-.36i
Chow Forecast Test: Forecast from 1/23/2006 to 5/12/2006
F-statistic
Log likelihood ratio
0.261150
21.55907
Prob. F(80,2357)
Prob. Chi-Square(80)
41
1.000000
1.000000
-.41
Dependent Variable: D(YIELD ON TREASURY SECURITIES ( 1-YEAR))
Method: Least Squares
Sample (adjusted): 10/07/1997 5/12/2006
Included observations: 2244 after adjustments
Newey-West HAC Standard Errors & Covariance (lag truncation=7)
Variable
Coefficient
Std. Error
t-Statistic
Prob.
-0.0028
0.0362
0.5619
0.0014
0.0140
0.0007
0.0206
0.0285
0.0007
0.0015
-4.1921
1.7601
19.7326
2.1091
9.6455
0.0000
0.0785
0.0000
0.0350
0.0000
CONSTANT
D(FEDERAL FUNDS RATE)
D(TREASURY FUTURES (2 YEAR))
DLOG(DOW-JONES FUTURES)*100
MONDAY
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
Durbin-Watson stat
0.6129
0.6122
0.0282
1.7849
4823.2
2.0611
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
F-statistic
Prob(F-statistic)
Chow Forecast Test: Forecast from 1/23/2006 to 5/12/2006
F-statistic
Log likelihood ratio
0.211010
17.47733
Prob. F(80,2159)
Prob. Chi-Square(80)
42
1.000000
1.000000
-0.0002
0.0453
-4.2943
-4.2816
886.1
0.0000
Dependent Variable: D(YIELD ON TREASURY SECURITIES ( 2-YEAR))
Method: Least Squares
Sample (adjusted): 10/09/1997 5/12/2006
Included observations: 2242 after adjustments
Convergence achieved after 4 iterations
Newey-West HAC Standard Errors & Covariance (lag truncation=7)
Variable
Coefficient
Std. Error
t-Statistic
Prob.
-0.0010
0.0488
0.8117
0.0007
0.0212
0.0243
-1.4142
2.2996
33.3736
0.1574
0.0216
0.0000
-0.0022
0.0033
0.0048
-0.0752
-0.0606
0.0010
0.0006
0.0015
0.0434
0.0349
-2.2084
5.2161
3.3047
-1.7313
-1.7348
0.0273
0.0000
0.0010
0.0835
0.0829
CONSTANT
D(FEDERAL FUNDS RATE)
D(TREASURY FUTURES (5 YEAR))
D(EXPECTED EURODOLLAR DEPOSIT
RATE )
DLOG(DOW-JONES FUTURES)*100
MONDAY
AR(1)
AR(2)
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
Durbin-Watson stat
0.7602
0.7595
0.0290
1.8723
4764.3
2.0013
Inverted AR Roots
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
F-statistic
Prob(F-statistic)
-.04-.24i
-.04+.24i
Chow Forecast Test: Forecast from 1/23/2006 to 5/12/2006
F-statistic
Log likelihood ratio
0.229367
19.01828
Prob. F(80,2154)
Prob. Chi-Square(80)
43
1.000000
1.000000
-0.0003
0.0590
-4.2429
-4.2225
1011.8
0.0000
Dependent Variable: D(YIELD ON TREASURY SECURITIES ( 3-YEAR))
Method: Least Squares
Sample (adjusted): 10/07/1997 5/12/2006
Included observations: 2244 after adjustments
Newey-West HAC Standard Errors & Covariance (lag truncation=7)
Variable
Coefficient
Std. Error
t-Statistic
Prob.
-0.0006
0.0019
0.8551
0.0007
0.0192
0.0410
-0.9431
0.0992
20.8813
0.3457
0.9210
0.0000
-0.0023
0.0032
0.0029
0.0012
0.0008
0.0016
-1.8490
4.0650
1.7799
0.0646
0.0000
0.0752
CONSTANT
D(FEDERAL FUNDS RATE)
D(TREASURY FUTURES (2 YEAR))
D(EXPECTED EURODOLLAR DEPOSIT
RATE )
DLOG(DOW-JONES FUTURES)*100
MONDAY
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
Durbin-Watson stat
0.7498
0.7492
0.0309
2.1361
4621.7
2.1474
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
F-statistic
Prob(F-statistic)
Chow Forecast Test: Forecast from 1/23/2006 to 5/12/2006
F-statistic
Log likelihood ratio
0.206568
17.11869
Prob. F(80,2158)
Prob. Chi-Square(80)
44
1.000000
1.000000
-0.0003
0.0617
-4.1138
-4.0985
1341.1
0.0000
Dependent Variable: D(YIELD ON TREASURY SECURITIES ( 5-YEAR))
Method: Least Squares
Sample (adjusted): 10/09/1997 5/12/2006
Included observations: 2242 after adjustments
Convergence achieved after 6 iterations
Newey-West HAC Standard Errors & Covariance (lag truncation=7)
Variable
Coefficient
Std. Error
t-Statistic
Prob.
-0.0008
0.0190
0.9082
0.0005
0.0167
0.0238
-1.5750
1.1318
38.1883
0.1154
0.2578
0.0000
-0.0017
0.0027
0.0040
-0.1470
-0.0669
0.0009
0.0006
0.0013
0.0518
0.0256
-1.8790
4.9532
3.0959
-2.8395
-2.6177
0.0604
0.0000
0.0020
0.0046
0.0089
CONSTANT
D(FEDERAL FUNDS RATE)
D(TREASURY FUTURES (5 YEAR))
D(EXPECTED EURODOLLAR DEPOSIT
RATE )
DLOG(DOW-JONES FUTURES)*100
MONDAY
AR(1)
AR(2)
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
Durbin-Watson stat
0.8415
0.8410
0.0247
1.3668
5117.1
2.0013
Inverted AR Roots
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
F-statistic
Prob(F-statistic)
-.07-.25i
-.07+.25i
Chow Forecast Test: Forecast from 1/23/2006 to 5/12/2006
F-statistic
Log likelihood ratio
0.169266
14.05056
Prob. F(80,2154)
Prob. Chi-Square(80)
45
1.000000
1.000000
-0.0004
0.0620
-4.5576
-4.5372
1693.9
0.0000
Dependent Variable: D(YIELD ON TREASURY SECURITIES ( 7-YEAR))
Method: Least Squares
Sample (adjusted): 10/07/1997 5/12/2006
Included observations: 2244 after adjustments
Newey-West HAC Standard Errors & Covariance (lag truncation=7)
Variable
Coefficient
Std. Error
t-Statistic
Prob.
-0.0004
-0.0072
0.0232
1.0816
0.0005
0.0117
0.0093
0.0290
-0.7907
-0.6124
2.4928
37.2807
0.4292
0.5403
0.0127
0.0000
-0.0021
0.0024
0.0024
0.0008
0.0005
0.0010
-2.4897
4.4949
2.4847
0.0129
0.0000
0.0130
CONSTANT
D(FEDERAL FUNDS RATE)
D(EXPECTED INFLATION (T-1))
D(TREASURY FUTURES (10-YEAR))
D(EXPECTED EURODOLLAR DEPOSIT
RATE )
DLOG(DOW-JONES FUTURES)*100
MONDAY
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
Durbin-Watson stat
0.8808
0.8804
0.0211
0.9979
5475.6
2.2260
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
F-statistic
Prob(F-statistic)
Chow Forecast Test: Forecast from 1/23/2006 to 5/12/2006
F-statistic
Log likelihood ratio
0.268208
22.21192
Prob. F(80,2157)
Prob. Chi-Square(80)
46
1.000000
1.000000
-0.0004
0.0611
-4.8740
-4.8562
2753.7
0.0000
Dependent Variable: D(YIELD ON TREASURY SECURITIES ( 10-YEAR))
Method: Least Squares
Sample (adjusted): 10/08/1997 5/12/2006
Included observations: 2243 after adjustments
Convergence achieved after 5 iterations
Newey-West HAC Standard Errors & Covariance (lag truncation=7)
Variable
Coefficient
Std. Error
t-Statistic
Prob.
-0.0006
-0.0195
0.0416
1.0125
0.0005
0.0085
0.0094
0.0267
-1.2693
-2.2822
4.4288
37.8675
0.2045
0.0226
0.0000
0.0000
-0.0021
0.0026
0.0036
-0.0752
0.0008
0.0005
0.0010
0.0300
-2.5228
4.8859
3.7109
-2.5097
0.0117
0.0000
0.0002
0.0122
CONSTANT
D(FEDERAL FUNDS RATE)
D(EXPECTED INFLATION (T-1))
D(TREASURY FUTURES (10-YEAR))
D(EXPECTED EURODOLLAR DEPOSIT
RATE )
DLOG(DOW-JONES FUTURES)*100
MONDAY
AR(1)
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
Durbin-Watson stat
0.8663
0.8659
0.0212
1.0015
5468.6
2.0001
Inverted AR Roots
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
F-statistic
Prob(F-statistic)
-.08
Chow Forecast Test: Forecast from 1/23/2006 to 5/12/2006
F-statistic
Log likelihood ratio
0.340336
28.16129
Prob. F(80,2155)
Prob. Chi-Square(80)
47
1.000000
1.000000
-0.0003
0.0578
-4.8691
-4.8487
2068.8
0.0000
Dependent Variable: D(YIELD ON TREASURY SECURITIES ( 20-YEAR))
Method: Least Squares
Sample (adjusted): 10/08/1997 5/12/2006
Included observations: 2243 after adjustments
Convergence achieved after 4 iterations
Newey-West HAC Standard Errors & Covariance (lag truncation=7)
Variable
Coefficient
Std. Error
t-Statistic
Prob.
0.0000
-0.0166
0.0150
0.9888
0.0002
0.0060
0.0059
0.0122
-0.0068
-2.7614
2.5581
80.8164
0.9946
0.0058
0.0106
0.0000
-0.0005
0.0009
-0.1609
0.0005
0.0003
0.0392
-1.1139
3.2951
-4.1060
0.2655
0.0010
0.0000
CONSTANT
D(FEDERAL FUNDS RATE)
D(EXPECTED INFLATION (T-1))
D(TREASURY FUTURES (30-YEAR))
D(EXPECTED EURODOLLAR DEPOSIT
RATE )
DLOG(DOW-JONES FUTURES)*100
AR(1)
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
Durbin-Watson stat
0.9332
0.9330
0.0134
0.4013
6494.4
2.0276
Inverted AR Roots
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
F-statistic
Prob(F-statistic)
-.16
Chow Forecast Test: Forecast from 1/23/2006 to 5/12/2006
F-statistic
Log likelihood ratio
0.487868
40.24136
Prob. F(80,2156)
Prob. Chi-Square(80)
48
0.999962
0.999940
-0.0004
0.0518
-5.7846
-5.7667
5206.4
0.0000
Dependent Variable: D(YIELD ON TREASURY SECURITIES ( 30-YEAR))
Method: Least Squares
Sample (adjusted): 2/04/1997 5/12/2006
Included observations: 2419 after adjustments
Convergence achieved after 5 iterations
Newey-West HAC Standard Errors & Covariance (lag truncation=8)
Variable
Coefficient
Std. Error
t-Statistic
Prob.
-0.0001
-0.0175
0.0318
0.8876
0.0003
0.0087
0.0085
0.0149
-0.1839
-2.0139
3.7273
59.5370
0.8541
0.0441
0.0002
0.0000
-0.0002
-0.0594
-0.1915
0.0006
0.0150
0.0354
-0.3846
-3.9603
-5.4156
0.7005
0.0001
0.0000
CONSTANT
D(FEDERAL FUNDS RATE)
D(EXPECTED INFLATION (T-1))
D(TREASURY FUTURES (30-YEAR))
D(EXPECTED EURODOLLAR DEPOSIT
RATE )
DUMMY30
AR(1)
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
Durbin-Watson stat
0.8199
0.8195
0.0209
1.0522
5929.4
2.0374
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
F-statistic
Prob(F-statistic)
Inverted AR Roots
-0.0006
0.0492
-4.8966
-4.8798
1830.5
0.0000
-.19
Chow Forecast Test: Forecast from 1/23/2006 to 5/12/2006
F-statistic
Log likelihood ratio
1.016164
82.85465
Prob. F(80,2333)
Prob. Chi-Square(80)
0.440397
0.391415
Notes:
1. Equations estimated for periods before February 10th do not include the dummy
variable, DUMMY30, which is equal to one for February 9th and 10th of 2006 and zero
for other periods.
2. Chow forecast test was conducted using the modified equation, without the dummy
variable.
49
APPENDIX B. ACTUAL, EX-ANTE FORECASTS AND ERRORS
obs
1/23/2006
1/24/2006
1/25/2006
1/26/2006
1/27/2006
1/30/2006
1/31/2006
2/1/2006
2/2/2006
2/3/2006
1-month
3.96
4.00
4.24
4.20
4.17
4.21
4.23
4.36
4.31
4.32
3-month
4.37
4.38
4.41
4.42
4.45
4.47
4.51
4.48
4.47
4.48
6-month
4.49
4.50
4.53
4.55
4.54
4.58
4.66
4.61
4.59
4.62
1-year
4.44
4.46
4.50
4.53
4.52
4.57
4.60
4.61
4.70
4.61
2-year
4.36
4.37
4.44
4.49
4.49
4.53
4.54
4.58
4.68
4.58
3-year
4.31
4.33
4.39
4.44
4.46
4.49
4.48
4.54
4.53
4.54
5-year
4.30
4.32
4.40
4.44
4.44
4.47
4.47
4.52
4.64
4.51
7-year
4.32
4.34
4.42
4.47
4.45
4.49
4.49
4.53
4.59
4.52
10-year
4.37
4.38
4.47
4.53
4.52
4.54
4.54
4.57
4.58
4.56
20-year
4.59
4.62
4.71
4.76
4.74
4.77
4.75
4.76
4.62
4.68
30-year
4.53
4.56
4.61
4.65
4.65
4.70
4.66
4.70
4.69
4.64
1-month
3.98
4.24
4.22
4.17
4.19
4.18
4.37
4.36
4.32
4.31
3-month
4.38
4.40
4.42
4.45
4.45
4.48
4.47
4.53
4.48
4.48
6-month
4.50
4.51
4.54
4.54
4.55
4.62
4.59
4.70
4.62
4.63
1-year
4.45
4.46
4.51
4.52
4.54
4.59
4.58
4.70
4.61
4.62
2-year
4.35
4.37
4.46
4.49
4.51
4.52
4.54
4.69
4.59
4.59
3-year
4.31
4.33
4.41
4.45
4.46
4.47
4.49
4.54
4.54
4.54
5-year
4.30
4.32
4.41
4.44
4.45
4.46
4.47
4.67
4.51
4.50
Forecast
Actual
7-year
4.31
4.34
4.43
4.46
4.47
4.49
4.49
4.59
4.53
4.51
10-year
4.36
4.40
4.49
4.53
4.52
4.54
4.53
4.59
4.57
4.54
20-year
4.59
4.63
4.72
4.76
4.75
4.77
4.74
4.59
4.76
4.70
30-year
4.54
4.53
4.62
4.66
4.70
4.67
4.69
4.69
4.68
4.64
Error (basis points)
1-month
-1.84
-24.18
1.56
3.15
-1.58
2.69
-14.48
0.42
-1.32
1.23
3-month
-0.83
-1.87
-1.27
-2.50
0.14
-0.80
4.32
-5.48
-1.29
-0.14
6-month
-0.75
-0.81
-0.70
0.80
-1.35
-4.23
6.94
-9.45
-2.74
-0.97
1-year
-0.51
-0.36
-1.16
0.69
-1.90
-2.29
2.22
-9.13
8.54
-1.36
2-year
1.28
0.09
-1.68
-0.19
-1.80
0.72
-0.46
-10.61
8.80
-1.03
3-year
0.15
-0.50
-1.73
-0.97
-0.33
1.56
-1.47
0.02
-0.52
0.01
5-year
0.12
0.22
-0.85
0.12
-0.76
0.91
0.14
-15.17
13.35
1.19
7-year
0.51
-0.39
-1.03
0.93
-1.98
0.29
0.05
-6.28
5.53
0.53
10-year
0.68
-1.54
-1.67
-0.39
0.17
0.23
0.72
-2.42
1.25
1.75
20-year
-0.19
-1.37
-1.44
-0.28
-0.60
-0.42
1.09
17.17
-14.31
-1.93
30-year
-1.05
Correct directional
change?
3.32
-1.33
-0.84
-5.50
3.47
-2.76
0.96
0.59
0.35
1-month
Y
Y
Y
Y
Y
N
Y
Y
Y
N
3-month
Y
Y
Y
Y
Y
Y
N
Y
Y
N
6-month
Y
Y
Y
Y
N
Y
N
Y
Y
Y
1-year
Y
Y
Y
Y
Y
Y
N
Y
Y
N
2-year
Y
Y
Y
Y
Y
Y
Y
Y
Y
N
3-year
Y
Y
Y
Y
Y
Y
Y
Y
N
Y
5-year
Y
Y
Y
Y
Y
Y
Y
Y
Y
N
7-year
Y
Y
Y
Y
N
Y
Y
Y
Y
Y
10-year
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
20-year
N
Y
Y
Y
Y
Y
Y
N
Y
Y
30-year
N
N
Y
Y
N
N
N
Y
Y
Y
50
obs
2/6/2006
2/7/2006
2/8/2006
2/9/2006
2/10/2006
2/13/2006
2/14/2006
2/15/2006
2/16/2006
2/17/2006
1-month
4.33
4.34
4.32
4.32
4.32
4.37
4.40
4.41
4.37
4.38
3-month
4.50
4.48
4.49
4.50
4.52
4.55
4.55
4.55
4.55
4.54
6-month
4.66
4.67
4.68
4.67
4.67
4.72
4.71
4.72
4.70
4.67
1-year
4.65
4.65
4.67
4.66
4.67
4.71
4.71
4.71
4.70
4.67
2-year
4.61
4.62
4.63
4.64
4.69
4.68
4.70
4.69
4.71
4.65
3-year
4.57
4.56
4.60
4.62
4.64
4.67
4.68
4.68
4.68
4.64
5-year
4.53
4.51
4.54
4.55
4.58
4.58
4.61
4.61
4.60
4.55
7-year
4.52
4.53
4.57
4.54
4.58
4.59
4.61
4.61
4.59
4.55
10-year
4.55
4.56
4.59
4.55
4.57
4.59
4.61
4.61
4.60
4.55
20-year
4.70
4.72
4.75
4.73
4.75
4.76
4.79
4.79
4.77
4.72
30-year
4.64
4.64
4.66
4.59
4.49
4.54
4.58
4.59
4.57
4.52
1-month
4.32
4.33
4.34
4.32
4.36
4.38
4.42
4.39
4.38
4.39
3-month
4.48
4.49
4.50
4.52
4.53
4.55
4.55
4.55
4.55
4.54
6-month
4.68
4.67
4.67
4.67
4.70
4.71
4.72
4.70
4.69
4.69
1-year
4.66
4.65
4.66
4.66
4.70
4.70
4.71
4.70
4.69
4.68
2-year
4.62
4.61
4.64
4.66
4.69
4.68
4.69
4.71
4.69
4.66
3-year
4.57
4.57
4.61
4.62
4.67
4.66
4.68
4.68
4.67
4.64
5-year
4.51
4.52
4.55
4.55
4.59
4.58
4.61
4.60
4.59
4.55
7-year
4.52
4.54
4.55
4.55
4.59
4.58
4.61
4.60
4.59
4.54
10-year
4.55
4.57
4.56
4.54
4.59
4.58
4.62
4.61
4.59
4.54
20-year
4.69
4.73
4.75
4.72
4.76
4.76
4.80
4.78
4.77
4.71
30-year
4.61
4.64
4.67
4.51
4.55
4.56
4.60
4.58
4.57
4.51
Forecast
Actual
Error (basis points)
1-month
0.69
1.07
-1.78
-0.15
-3.61
-0.62
-1.73
1.94
-1.28
3-month
1.76
-1.31
-0.56
-1.82
-1.26
-0.08
-0.31
-0.01
-0.04
-0.98
0.39
6-month
-2.18
-0.10
0.75
-0.13
-2.62
0.53
-0.78
1.52
0.58
-1.65
1-year
-1.29
-0.03
0.72
0.42
-3.06
0.82
-0.15
0.98
0.80
-0.92
2-year
-0.66
0.99
-0.78
-1.84
-0.41
0.40
1.37
-2.08
1.54
-0.57
3-year
-0.38
-1.41
-0.91
-0.04
-3.24
0.84
-0.13
0.15
1.23
0.31
5-year
1.99
-0.58
-0.65
0.05
-0.88
0.23
-0.49
0.77
0.64
0.21
7-year
-0.26
-0.99
1.71
-1.28
-0.88
0.83
-0.38
0.56
0.24
0.53
10-year
-0.03
-1.10
3.45
0.93
-2.06
0.82
-1.47
0.40
1.32
0.89
20-year
1.09
-0.75
0.36
0.85
-1.37
0.39
-1.28
0.76
0.39
0.59
30-year
2.80
0.37
-0.83
7.76
-6.20
-1.85
-1.86
0.76
0.42
1.18
Y
Y
Y
Y
Y
Y
Y
Correct directional change?
1-month
Y
Y
N
3-month
Y
N
Y
Y
N
Y
N
N
N
Y
6-month
Y
Y
Y
N
Y
Y
Y
Y
Y
N
1-year
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
2-year
Y
Y
Y
Y
Y
Y
Y
N
Y
Y
3-year
Y
N
Y
Y
Y
Y
Y
Y
N
Y
5-year
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
7-year
Y
Y
Y
N
Y
Y
Y
Y
Y
Y
10-year
Y
Y
N
Y
Y
Y
Y
Y
Y
Y
20-year
N
Y
Y
Y
Y
Y
Y
Y
Y
Y
30-year
Y
Y
Y
Y
N
N
Y
Y
Y
Y
51
obs
2/20/2006
2/21/2006
2/22/2006
2/23/2006
2/24/2006
2/27/2006
2/28/2006
3/1/2006
3/2/2006
3/3/2006
1-month
4.40
4.41
4.41
4.42
4.44
4.46
4.50
4.46
4.43
4.46
3-month
4.56
4.54
4.56
4.57
4.59
4.62
4.61
4.62
4.60
4.62
6-month
4.71
4.70
4.72
4.71
4.72
4.75
4.74
4.74
4.75
4.76
1-year
4.69
4.69
4.72
4.70
4.72
4.74
4.73
4.74
4.74
4.76
2-year
4.66
4.68
4.69
4.71
4.72
4.76
4.70
4.71
4.74
4.74
3-year
4.64
4.66
4.67
4.68
4.70
4.71
4.67
4.69
4.69
4.75
5-year
4.55
4.57
4.57
4.61
4.62
4.66
4.61
4.63
4.66
4.70
7-year
4.54
4.56
4.55
4.59
4.58
4.62
4.56
4.60
4.64
4.69
10-year
4.54
4.56
4.55
4.57
4.56
4.60
4.55
4.58
4.63
4.67
20-year
4.71
4.72
4.69
4.71
4.70
4.73
4.69
4.74
4.79
4.84
30-year
4.51
4.52
4.51
4.51
4.51
4.54
4.51
4.54
4.60
4.65
1-month
4.39
4.42
4.44
4.44
4.45
4.48
4.47
4.45
4.45
4.45
3-month
4.54
4.56
4.57
4.59
4.60
4.62
4.62
4.60
4.62
4.62
6-month
4.69
4.73
4.70
4.73
4.73
4.76
4.74
4.75
4.75
4.75
1-year
4.68
4.73
4.69
4.73
4.73
4.76
4.73
4.74
4.74
4.75
2-year
4.66
4.71
4.68
4.72
4.74
4.74
4.69
4.71
4.72
4.76
3-year
4.64
4.68
4.66
4.70
4.70
4.71
4.67
4.68
4.72
4.75
5-year
4.55
4.59
4.57
4.63
4.64
4.66
4.61
4.63
4.68
4.71
7-year
4.54
4.58
4.55
4.58
4.60
4.61
4.57
4.60
4.66
4.69
10-year
4.54
4.57
4.53
4.56
4.58
4.59
4.55
4.59
4.64
4.68
20-year
4.71
4.72
4.68
4.70
4.71
4.74
4.70
4.74
4.80
4.84
30-year
4.51
4.53
4.48
4.51
4.52
4.55
4.51
4.56
4.62
4.66
Forecast
Actual
Error (basis points)
1-month
1.45
-0.64
-3.25
-1.93
-0.78
-1.61
2.72
1.12
-2.07
0.63
3-month
1.52
-1.74
-1.39
-1.70
-1.48
0.05
-0.65
2.30
-1.93
0.14
6-month
1.79
-3.27
1.81
-2.07
-0.84
-1.04
-0.22
-0.51
-0.06
0.84
1-year
1.12
-3.71
2.89
-2.53
-0.51
-1.65
0.29
0.20
0.38
0.53
2-year
0.42
-3.22
1.23
-0.55
-2.17
1.61
0.76
-0.13
1.53
-1.85
3-year
0.21
-1.66
0.74
-1.60
-0.21
-0.45
-0.06
1.47
-3.19
-0.38
5-year
0.36
-1.91
-0.04
-2.05
-1.58
-0.40
0.31
-0.14
-2.13
-1.01
7-year
0.22
-1.81
0.46
0.81
-1.60
0.86
-0.59
-0.02
-1.54
0.26
10-year
0.43
-0.97
1.57
0.63
-1.60
0.79
-0.31
-1.29
-0.89
-1.02
20-year
0.14
0.26
1.46
0.88
-0.54
-0.63
-0.58
-0.20
-1.45
-0.16
30-year
0.27
-0.86
2.50
-0.15
-0.83
-0.84
-0.10
-1.59
-2.13
-0.59
Correct directional change?
1-month
Y
Y
N
N
Y
Y
N
Y
N
Y
3-month
Y
Y
N
Y
N
Y
N
N
Y
Y
6-month
Y
Y
Y
Y
N
Y
Y
Y
N
Y
1-year
Y
Y
Y
Y
N
Y
Y
Y
Y
Y
2-year
Y
Y
Y
Y
N
Y
Y
Y
Y
Y
3-year
Y
Y
Y
Y
N
Y
Y
Y
Y
Y
5-year
Y
Y
Y
Y
N
Y
Y
Y
Y
Y
7-year
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
10-year
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
20-year
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
30-year
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
52
obs
3/6/2006
3/7/2006
3/8/2006
3/9/2006
3/10/2006
3/13/2006
3/14/2006
3/15/2006
3/16/2006
3/17/2006
1-month
4.47
4.46
4.46
4.43
4.45
4.47
4.46
4.48
4.47
4.49
3-month
4.64
4.60
4.60
4.58
4.60
4.64
4.59
4.59
4.62
4.61
6-month
4.77
4.77
4.76
4.76
4.78
4.80
4.79
4.80
4.77
4.77
1-year
4.77
4.77
4.76
4.75
4.77
4.78
4.75
4.75
4.73
4.72
2-year
4.79
4.77
4.76
4.72
4.74
4.75
4.67
4.68
4.64
4.64
3-year
4.77
4.77
4.78
4.76
4.80
4.80
4.74
4.73
4.66
4.63
5-year
4.74
4.76
4.75
4.74
4.77
4.78
4.70
4.70
4.63
4.62
7-year
4.73
4.74
4.75
4.73
4.76
4.78
4.71
4.71
4.64
4.63
10-year
4.72
4.73
4.74
4.72
4.75
4.77
4.70
4.73
4.67
4.67
20-year
4.89
4.91
4.91
4.90
4.93
4.94
4.89
4.93
4.87
4.89
30-year
4.70
4.72
4.72
4.71
4.73
4.75
4.71
4.74
4.70
4.72
1-month
4.44
4.47
4.45
4.44
4.46
4.45
4.49
4.50
4.49
4.50
3-month
4.60
4.60
4.58
4.60
4.62
4.61
4.59
4.63
4.62
4.64
6-month
4.77
4.77
4.77
4.77
4.78
4.83
4.80
4.81
4.77
4.78
1-year
4.77
4.77
4.76
4.76
4.77
4.80
4.75
4.77
4.72
4.74
2-year
4.77
4.77
4.72
4.72
4.74
4.74
4.66
4.69
4.62
4.65
3-year
4.77
4.79
4.77
4.77
4.80
4.81
4.72
4.72
4.62
4.64
5-year
4.76
4.76
4.75
4.75
4.77
4.78
4.68
4.69
4.60
4.62
7-year
4.74
4.75
4.74
4.74
4.76
4.78
4.69
4.70
4.61
4.63
10-year
4.74
4.74
4.73
4.74
4.76
4.77
4.71
4.73
4.65
4.68
20-year
4.91
4.91
4.91
4.91
4.93
4.95
4.89
4.93
4.86
4.89
30-year
4.72
4.72
4.72
4.72
4.74
4.77
4.71
4.75
4.70
4.72
Forecast
Actual
Error (basis points)
1-month
2.54
-1.01
0.87
-1.15
-1.41
2.33
-2.81
-1.94
-1.80
3-month
3.92
-0.38
2.02
-2.19
-2.29
2.77
0.43
-4.03
0.06
-0.62
-2.54
6-month
0.43
-0.45
-0.71
-0.58
-0.34
-3.38
-0.88
-1.00
0.08
-1.16
1-year
0.17
-0.25
0.30
-0.55
0.50
-1.86
-0.03
-1.52
1.13
-1.66
2-year
1.78
0.11
4.11
-0.22
0.04
1.31
0.74
-1.47
1.53
-1.11
3-year
-0.11
-1.90
1.14
-0.54
-0.13
-0.93
1.62
1.39
4.37
-0.91
5-year
-2.16
-0.29
-0.19
-0.57
-0.14
0.42
1.85
0.78
3.21
0.34
7-year
-0.67
-1.34
0.69
-1.34
-0.44
-0.49
1.82
1.31
2.68
0.08
10-year
-1.87
-0.50
0.61
-2.34
-0.71
0.47
-0.70
0.12
2.09
-1.04
20-year
-2.32
-0.48
0.45
-0.52
-0.43
-0.73
0.15
-0.38
1.40
-0.49
30-year
-1.82
-0.38
0.34
-0.55
-0.67
-1.93
0.48
-0.70
-0.12
-0.10
Y
Y
N
Y
N
Y
Y
Correct directional change?
1-month
N
Y
Y
3-month
N
N
N
N
N
N
Y
N
Y
N
6-month
Y
N
N
N
Y
Y
Y
Y
Y
N
1-year
Y
N
Y
N
Y
Y
Y
Y
Y
Y
2-year
Y
Y
Y
N
Y
Y
Y
Y
Y
Y
3-year
Y
Y
Y
N
Y
Y
Y
Y
Y
Y
5-year
Y
N
Y
N
Y
Y
Y
Y
Y
Y
7-year
Y
N
Y
N
Y
Y
Y
Y
Y
Y
10-year
Y
N
Y
N
Y
Y
Y
Y
Y
Y
20-year
Y
N
Y
N
Y
Y
Y
Y
Y
Y
30-year
Y
N
Y
N
Y
Y
Y
Y
Y
Y
53
obs
3/20/2006
3/21/2006
3/22/2006
3/23/2006
3/24/2006
3/27/2006
3/28/2006
3/29/2006
3/30/2006
3/31/2006
1-month
4.51
4.59
4.66
4.65
4.66
4.68
4.71
4.70
4.67
4.67
3-month
4.65
4.67
4.69
4.70
4.66
4.67
4.66
4.65
4.63
4.60
6-month
4.80
4.81
4.82
4.82
4.78
4.81
4.86
4.83
4.84
4.83
1-year
4.75
4.78
4.80
4.79
4.77
4.78
4.81
4.82
4.84
4.83
2-year
4.65
4.70
4.72
4.78
4.71
4.74
4.79
4.82
4.84
4.83
3-year
4.65
4.68
4.72
4.74
4.69
4.69
4.75
4.80
4.83
4.83
5-year
4.62
4.67
4.68
4.73
4.66
4.69
4.76
4.80
4.82
4.82
7-year
4.61
4.68
4.68
4.75
4.66
4.68
4.76
4.82
4.83
4.82
10-year
4.66
4.72
4.70
4.75
4.67
4.69
4.76
4.81
4.84
4.85
20-year
4.87
4.91
4.90
4.93
4.88
4.89
4.96
5.01
5.05
5.07
30-year
4.71
4.74
4.73
4.75
4.70
4.72
4.78
4.82
4.87
4.89
1-month
4.56
4.67
4.67
4.66
4.66
4.66
4.71
4.69
4.67
4.65
3-month
4.66
4.69
4.69
4.67
4.65
4.63
4.65
4.63
4.61
4.63
6-month
4.79
4.82
4.81
4.81
4.78
4.80
4.83
4.83
4.84
4.81
1-year
4.74
4.79
4.78
4.80
4.76
4.77
4.82
4.83
4.84
4.82
2-year
4.65
4.72
4.74
4.77
4.72
4.72
4.81
4.82
4.84
4.82
3-year
4.62
4.71
4.72
4.74
4.67
4.69
4.79
4.81
4.84
4.83
5-year
4.61
4.68
4.69
4.73
4.66
4.69
4.79
4.79
4.83
4.82
7-year
4.62
4.69
4.70
4.73
4.66
4.69
4.79
4.79
4.83
4.83
10-year
4.66
4.71
4.70
4.73
4.67
4.70
4.79
4.81
4.86
4.86
20-year
4.87
4.91
4.91
4.93
4.87
4.91
4.98
5.02
5.07
5.07
30-year
4.70
4.74
4.73
4.75
4.70
4.73
4.80
4.84
4.89
4.90
Forecast
Actual
Error (basis points)
1-month
-4.72
-8.39
-0.86
-0.97
-0.31
1.52
0.16
1.10
0.07
2.15
3-month
-0.69
-1.81
-0.19
2.54
1.15
4.08
1.38
1.95
1.95
-2.72
6-month
0.76
-0.71
1.10
0.59
0.25
0.70
3.20
-0.11
-0.42
2.45
1-year
1.34
-1.46
1.71
-0.92
0.51
1.42
-0.57
-0.77
0.04
1.26
2-year
-0.28
-1.86
-1.64
0.70
-0.95
2.26
-1.59
0.38
0.44
1.22
3-year
2.55
-3.22
0.41
0.11
1.82
0.22
-4.33
-1.04
-1.42
0.41
5-year
0.77
-1.03
-0.56
0.25
0.49
-0.45
-2.65
1.04
-0.99
-0.02
7-year
-0.67
-0.96
-1.58
2.02
0.29
-0.61
-3.30
2.57
-0.45
-0.92
10-year
0.46
0.59
0.42
1.72
-0.16
-0.72
-3.15
0.20
-1.72
-0.98
20-year
0.29
0.34
-0.86
0.44
0.92
-1.55
-1.56
-1.03
-1.51
0.13
30-year
0.55
-0.11
0.05
0.36
0.48
-0.87
-2.06
-1.55
-1.90
-0.99
Correct directional change?
1-month
Y
Y
N
Y
N
Y
Y
Y
Y
N
3-month
Y
Y
N
N
Y
N
Y
Y
Y
N
6-month
Y
Y
N
Y
Y
Y
Y
N
Y
Y
1-year
Y
Y
N
Y
Y
Y
Y
Y
Y
Y
2-year
N
Y
Y
Y
Y
Y
Y
Y
Y
Y
3-year
N
Y
Y
Y
Y
Y
Y
Y
Y
Y
5-year
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
7-year
Y
Y
N
Y
Y
Y
Y
Y
Y
N
10-year
Y
Y
Y
Y
Y
Y
Y
Y
Y
N
20-year
Y
Y
N
Y
Y
Y
Y
Y
Y
Y
30-year
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
54
obs
4/3/2006
4/4/2006
4/5/2006
4/6/2006
4/7/2006
4/10/2006
4/11/2006
4/12/2006
4/13/2006
4/14/2006
1-month
4.67
4.68
4.63
4.60
4.66
4.65
4.66
4.62
4.60
4.54
3-month
4.65
4.66
4.67
4.67
4.69
4.71
4.68
4.70
4.70
4.70
6-month
4.84
4.84
4.83
4.83
4.87
4.87
4.88
4.89
4.92
4.94
1-year
4.85
4.84
4.83
4.83
4.88
4.87
4.88
4.90
4.92
4.95
2-year
4.84
4.84
4.81
4.84
4.88
4.89
4.87
4.91
4.94
4.96
3-year
4.86
4.82
4.80
4.81
4.87
4.89
4.87
4.89
4.92
4.96
5-year
4.84
4.83
4.79
4.82
4.89
4.89
4.86
4.90
4.95
4.96
7-year
4.85
4.84
4.81
4.84
4.91
4.92
4.89
4.92
4.98
5.00
10-year
4.88
4.87
4.84
4.87
4.95
4.97
4.94
4.97
5.02
5.05
20-year
5.08
5.07
5.07
5.12
5.18
5.20
5.18
5.21
5.27
5.28
30-year
4.91
4.90
4.89
4.94
5.01
5.04
5.02
5.04
5.09
5.11
1-month
4.66
4.64
4.62
4.65
4.64
4.64
4.63
4.62
4.54
4.54
3-month
4.67
4.68
4.67
4.68
4.69
4.69
4.70
4.70
4.70
4.70
6-month
4.86
4.85
4.83
4.85
4.85
4.89
4.88
4.91
4.94
4.94
1-year
4.86
4.85
4.82
4.85
4.86
4.89
4.88
4.91
4.95
4.95
2-year
4.86
4.84
4.81
4.84
4.89
4.89
4.88
4.91
4.96
4.96
3-year
4.85
4.83
4.79
4.83
4.89
4.89
4.86
4.90
4.96
4.96
5-year
4.85
4.82
4.79
4.84
4.89
4.89
4.86
4.91
4.97
4.97
7-year
4.86
4.84
4.80
4.86
4.92
4.92
4.88
4.93
5.00
5.00
10-year
4.88
4.87
4.84
4.90
4.97
4.97
4.93
4.98
5.05
5.05
20-year
5.08
5.09
5.07
5.13
5.20
5.21
5.17
5.22
5.28
5.28
30-year
4.90
4.91
4.90
4.96
5.04
5.04
5.00
5.05
5.11
5.11
Forecast
Actual
Error (basis points)
1-month
0.60
3.86
0.73
-4.88
1.75
1.20
2.83
0.33
6.28
0.25
3-month
-1.97
-1.68
0.00
-0.85
-0.45
1.54
-1.70
0.09
-0.03
-0.29
6-month
-1.92
-0.59
0.40
-1.60
1.60
-2.31
-0.22
-2.04
-2.47
-0.46
1-year
-0.87
-0.97
0.90
-1.89
1.57
-1.86
-0.32
-1.38
-2.65
-0.28
2-year
-1.89
0.15
0.44
-0.38
-0.71
0.01
-1.43
0.01
-1.74
-0.20
3-year
1.20
-0.78
1.49
-2.06
-1.68
0.16
1.21
-1.12
-3.56
-0.05
5-year
-0.91
0.92
0.31
-1.98
-0.44
-0.15
0.41
-1.47
-2.45
-0.50
7-year
-0.51
0.48
0.65
-2.35
-0.57
-0.04
0.98
-0.73
-2.45
-0.02
10-year
0.37
-0.37
-0.16
-2.62
-2.12
-0.03
1.17
-0.93
-2.83
-0.26
20-year
-0.08
-1.67
-0.11
-1.29
-1.50
-1.19
1.33
-1.08
-1.36
-0.18
30-year
0.65
-1.43
-1.05
-1.92
-3.13
-0.50
1.84
-1.38
-1.97
-0.32
N
Y
N
Y
Y
Y
Correct directional change?
1-month
Y
N
Y
N
3-month
Y
N
Y
Y
Y
Y
N
Y
N
N
6-month
Y
Y
Y
Y
Y
Y
Y
Y
Y
N
1-year
Y
Y
Y
Y
Y
Y
Y
Y
Y
N
2-year
Y
Y
Y
Y
Y
Y
Y
Y
Y
N
3-year
Y
Y
Y
Y
Y
Y
Y
Y
Y
N
5-year
Y
Y
Y
Y
Y
N
Y
Y
Y
N
7-year
Y
Y
Y
Y
Y
N
Y
Y
Y
N
10-year
Y
Y
Y
Y
Y
N
Y
Y
Y
N
20-year
Y
N
Y
Y
Y
N
Y
Y
Y
N
30-year
Y
N
Y
Y
Y
N
Y
Y
Y
N
55
obs
4/17/2006
4/18/2006
4/19/2006
4/20/2006
4/21/2006
4/24/2006
4/25/2006
4/26/2006
4/27/2006
4/28/2006
1-month
4.55
4.56
4.53
4.52
4.55
4.59
4.60
4.62
4.62
4.64
3-month
4.72
4.71
4.72
4.73
4.73
4.76
4.76
4.79
4.78
4.77
6-month
4.94
4.90
4.90
4.90
4.90
4.91
4.95
4.97
4.95
4.91
1-year
4.94
4.90
4.89
4.90
4.91
4.90
4.95
4.97
4.94
4.90
2-year
4.93
4.88
4.86
4.88
4.89
4.88
4.94
4.98
4.94
4.88
3-year
4.93
4.86
4.88
4.89
4.90
4.88
4.92
4.98
4.93
4.88
5-year
4.94
4.89
4.89
4.92
4.92
4.90
4.96
5.01
4.97
4.92
7-year
4.97
4.92
4.95
4.97
4.96
4.93
5.01
5.05
5.02
4.98
10-year
5.02
4.98
5.02
5.05
5.03
4.99
5.05
5.10
5.08
5.07
20-year
5.25
5.23
5.28
5.29
5.26
5.22
5.29
5.33
5.33
5.31
30-year
5.09
5.06
5.11
5.13
5.11
5.08
5.13
5.17
5.17
5.17
1-month
4.55
4.54
4.54
4.55
4.58
4.58
4.63
4.65
4.64
4.60
3-month
4.72
4.72
4.73
4.73
4.75
4.75
4.79
4.79
4.78
4.77
6-month
4.93
4.90
4.90
4.90
4.90
4.93
4.96
4.98
4.93
4.91
1-year
4.93
4.88
4.89
4.90
4.90
4.92
4.95
4.98
4.93
4.90
2-year
4.91
4.84
4.86
4.89
4.90
4.89
4.95
4.99
4.91
4.87
3-year
4.91
4.86
4.87
4.89
4.89
4.88
4.94
4.99
4.92
4.87
5-year
4.93
4.87
4.91
4.92
4.92
4.90
4.98
5.02
4.95
4.92
7-year
4.96
4.92
4.96
4.97
4.95
4.94
5.02
5.06
5.00
4.98
10-year
5.01
4.99
5.04
5.04
5.01
4.99
5.07
5.12
5.09
5.07
20-year
5.25
5.23
5.29
5.29
5.25
5.22
5.31
5.34
5.32
5.31
30-year
5.08
5.07
5.13
5.14
5.10
5.07
5.16
5.18
5.18
5.17
Forecast
Actual
Error (basis points)
1-month
-0.09
2.48
-0.78
-2.89
-2.56
1.06
-2.63
-2.58
-1.59
3.92
3-month
-0.41
-0.97
-1.01
0.06
-1.93
1.48
-3.32
0.30
0.02
-0.01
6-month
1.06
-0.02
0.46
0.30
0.19
-1.93
-1.35
-0.66
1.65
-0.16
1-year
0.97
1.53
0.09
-0.24
0.63
-1.79
-0.37
-0.69
0.84
0.43
2-year
2.38
3.59
0.20
-1.32
-1.33
-0.52
-1.02
-0.87
3.25
1.19
3-year
1.66
0.45
0.93
-0.15
1.18
-0.16
-1.71
-1.07
0.95
1.35
5-year
1.03
1.97
-1.60
0.39
-0.22
0.41
-2.20
-0.72
1.63
-0.08
7-year
1.06
0.33
-0.89
0.33
0.67
-1.09
-1.19
-0.79
2.18
-0.43
10-year
1.34
-1.29
-2.17
1.20
1.74
0.28
-1.70
-2.14
-0.74
-0.29
20-year
0.43
0.39
-1.08
0.01
0.98
0.28
-2.05
-1.12
1.20
0.05
30-year
0.76
-0.51
-1.71
-1.12
1.03
0.65
-2.70
-0.59
-0.62
-0.11
Correct directional change?
1-month
Y
N
N
N
Y
Y
Y
N
Y
Y
3-month
Y
N
N
Y
Y
Y
Y
Y
Y
Y
6-month
N
Y
Y
Y
Y
Y
Y
Y
Y
Y
1-year
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
2-year
Y
Y
Y
Y
N
Y
Y
Y
Y
Y
3-year
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
5-year
Y
Y
Y
Y
N
Y
Y
Y
Y
Y
7-year
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
10-year
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
20-year
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
30-year
Y
Y
Y
N
Y
Y
Y
Y
N
Y
56
obs
5/1/2006
5/2/2006
5/3/2006
5/4/2006
5/5/2006
5/8/2006
5/9/2006
5/10/2006
5/11/2006
5/12/2006
1-month
4.62
4.63
4.65
4.63
4.61
4.62
4.66
4.74
4.67
4.64
3-month
4.80
4.82
4.81
4.82
4.80
4.85
4.87
4.90
4.88
4.82
6-month
4.95
4.98
4.98
5.00
5.00
5.02
5.03
5.07
5.03
4.99
1-year
4.94
4.97
4.97
4.99
4.98
5.00
5.01
5.03
5.02
4.99
2-year
4.92
4.93
4.94
4.95
4.94
4.95
4.97
4.99
5.01
5.01
3-year
4.92
4.95
4.95
4.98
4.97
4.97
4.99
4.99
4.99
5.02
5-year
4.98
4.98
5.01
5.02
5.00
5.00
5.01
5.03
5.03
5.06
7-year
5.04
5.03
5.06
5.07
5.04
5.03
5.05
5.06
5.07
5.11
10-year
5.13
5.13
5.15
5.16
5.12
5.12
5.12
5.13
5.14
5.17
20-year
5.36
5.36
5.38
5.38
5.35
5.34
5.34
5.34
5.37
5.43
30-year
5.21
5.21
5.23
5.24
5.20
5.19
5.19
5.19
5.22
5.27
1-month
4.61
4.66
4.65
4.61
4.61
4.64
4.72
4.69
4.64
4.64
3-month
4.82
4.81
4.82
4.80
4.83
4.87
4.88
4.88
4.82
4.85
6-month
4.98
4.98
5.00
5.01
5.00
5.03
5.03
5.03
4.99
5.00
1-year
4.97
4.96
4.98
5.00
4.98
5.01
5.01
5.02
4.99
5.00
2-year
4.94
4.92
4.94
4.97
4.94
4.97
4.97
5.01
4.99
5.01
3-year
4.95
4.94
4.96
4.99
4.96
4.99
4.98
5.00
5.01
5.03
5-year
4.99
4.98
5.01
5.03
4.99
5.01
5.01
5.03
5.04
5.08
7-year
5.04
5.03
5.06
5.08
5.03
5.05
5.05
5.06
5.07
5.12
10-year
5.14
5.12
5.15
5.16
5.12
5.12
5.13
5.13
5.14
5.19
20-year
5.38
5.35
5.38
5.38
5.35
5.34
5.35
5.34
5.38
5.44
30-year
5.23
5.20
5.24
5.23
5.20
5.19
5.20
5.19
5.23
5.29
Forecast
Actual
Error (basis points)
1-month
0.62
-3.08
0.30
2.24
-0.06
-1.69
-5.95
4.76
2.87
0.22
3-month
-1.97
0.72
-0.96
2.02
-3.11
-2.23
-0.81
2.40
6.19
-2.89
6-month
-3.09
-0.48
-1.83
-0.68
-0.48
-0.63
-0.48
4.01
3.51
-1.01
1-year
-2.70
0.61
-1.40
-0.83
0.48
-1.43
-0.21
0.55
2.56
-0.77
2-year
-1.56
1.21
0.42
-1.99
0.23
-2.01
0.21
-1.96
2.00
0.06
3-year
-2.82
0.78
-0.68
-0.83
1.09
-1.95
1.03
-0.58
-1.66
-1.27
5-year
-1.26
-0.04
-0.32
-1.03
0.83
-0.85
0.40
-0.49
-0.72
-1.79
7-year
0.27
-0.33
0.16
-1.34
1.03
-1.67
0.24
-0.44
0.43
-1.27
10-year
-0.96
0.75
-0.07
-0.43
0.23
0.46
-0.68
0.19
0.28
-1.52
20-year
-2.13
1.09
0.35
-0.17
-0.42
-0.02
-0.56
0.04
-1.17
-1.30
30-year
-1.52
1.31
-0.95
0.54
0.00
0.09
-0.61
0.07
-1.33
-1.78
Y
Y
Y
N
Y
Y
N
Y
Y
Correct directional change?
1-month
Y
3-month
Y
Y
Y
N
N
Y
Y
Y
N
Y
6-month
Y
N
Y
Y
Y
Y
N
Y
Y
N
1-year
Y
Y
Y
Y
Y
Y
N
Y
Y
Y
2-year
Y
Y
Y
Y
Y
Y
Y
Y
N
Y
3-year
Y
Y
Y
Y
Y
Y
N
Y
N
Y
5-year
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
7-year
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
10-year
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
20-year
Y
Y
Y
N
Y
Y
Y
Y
Y
Y
30-year
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
57
APPENDIX C. DATA SOURCES & DEFINITIONS
DF01
SELECTED INTEREST RATES\Average Effective Rate of Federal
Funds\UNITS Percent Per Annum\SOURCE: Federal Reserve, H.15
(Selected Interest Rates)
DF29
YIELD ON U.S. TREASURY SECURITIES WITH\CONSTANT MATURITY\1Month\UNITS Percent\SOURCE: Treasury Dept (Treasury Yield Curve
Rates)
DF78
BOND YIELDS\Yield on U.S. Treasury Securities Adjusted to Constant
Maturity\3-Month\UNITS Percent\SOURCE: Federal Reserve (H.15,
Selected Interest Rates)
DF79
BOND YIELDS\Yield on U.S. Treasury Securities Adjusted to Constant
Maturity\6-Month\UNITS Percent\SOURCE: Federal Reserve (H.15,
Selected Interest Rates)
DF23
BOND YIELDS\Yield on U.S. Treasury Securities Adjusted to Constant
Maturity\1-Year\UNITS Percent\SOURCE: Federal Reserve (H.15, Selected
Interest Rates)
DF24
BOND YIELDS\Yield on U.S. Treasury Securities Adjusted to Constant
Maturity\2-Years\UNITS Percent\SOURCE: Federal Reserve (H.15,
Selected Interest Rates)
DF25
BOND YIELDS\Yield on U.S. Treasury Securities Adjusted to Constant
Maturity\3-Years\UNITS Percent\SOURCE: Federal Reserve (H.15,
Selected Interest Rates)
DF26
BOND YIELDS\Yield on U.S. Treasury Securities Adjusted to Constant
Maturity\5-Years\UNITS Percent\SOURCE: Federal Reserve (H.15,
Selected Interest Rates)
DF27
BOND YIELDS\Yield on U.S. Treasury Securities Adjusted to Constant
Maturity\7-Years\UNITS Percent\SOURCE: Federal Reserve (H.15, Selected
Interest Rates)
DF28
BOND YIELDS\Yield on U.S. Treasury Securities Adjusted to Constant
Maturity\10-Years\UNITS Percent\SOURCE: Federal Reserve (H.15,
Selected Interest Rates)
DF73
DF30A
BOND YIELDS\Yield on U.S. Treasury Securities Adjusted to Constant
Maturity\20-Years\UNITS Percent\SOURCE: Federal Reserve (H.15,
Selected Interest Rates)
BOND YIELDS\Yield on U.S. Treasury Securities Adjusted to Constant
Maturity\30-Years\UNITS Percent\SOURCE: Calculated by DRI-WEFA by
adding an extrapolation value provided by the Federal Reserve to the 20 year
Constant Maturity rate (DF73) published in the H.15 press report.\Prior to
6/1/2004 this series was calculated from the Long Term Treasury Constant
maturity rate (DF301).
DF01A
SELECTED INTEREST RATES\Federal Funds Rate Target\UNITS Percent
Per Annum\SOURCE: Federal Reserve Bank of New York
DF144
EXCHANGE RATES\DAILY NOON BUYING RATES\UNITED
KINGDOM\UNITS US DOLLARS PER POUND\SOURCE: FEDERAL
RESERVE, H.10 (FOREIGN INTEREST RATES)
DF152
SELECTED INTEREST RATES\EURODOLLAR DEPOSITS, 6MONTH\UNITS PERCENT PER ANNUM\SOURCE: FR, H.15 (SELECTED
INTEREST RATES)
58
DF233
BOND YIELDS\Yield on U.S. Treasury Securities Adjusted to Constant
Maturity, Inflation Indexed\10 Year\UNITS Percent\SOURCE: Federal
Reserve (H.15, Selected Interest Rates)
DF69
GOLD PRICE, LONDON P.M. FIXING\US $ AND CENT PER TROY
OUNCE\SOURCE: DAILY PRESS
DF70
INTERNATIONAL FINANCIAL INDICATORS, DETAILS\Silver\UNITS
Dollars per Troy Ounce\SOURCE: Financial Times (London Bullion Market)
DSPWTXI
PRICES\DOMESTIC SPOT MARKET\WEST TEXAS INTERMEDIATE
CUSH\UNITS DOLLARS PER BARREL\SOURCE: DAILY PRESS
PCFWTC
PRICES\FUTURES\CRUDE OIL, LIGHT SWEET (NYM)\CLOSE FOR THE
DAY\UNITS DOLLARS PER BARREL\SOURCE: DAILY PRESS
DF24FUTURES
2-year treasury yield futures, Source: Bloomberg, Decision Economics, Inc.
DF26FUTURES
5-year treasury yield futures, Source: Bloomberg, Decision Economics, Inc.
DF28FUTURES
10-year treasury yield futures, Source: Bloomberg, Decision Economics, Inc.
DF30FUTURES
30-year treasury yield futures, Source: Bloomberg, Decision Economics, Inc.
DF36FUTURES
Dow-Jones industrialist futures, Source: Bloomberg, Decision Economics, Inc.
______________________________________________________________________
Source: Global Insight Daily Financial Data Bank, except data on futures, which are
available from Bloomberg, and provided by Decision Economics, Inc. researcher Josh
White.
59