Cyclical Classification of Commodities Prices
and the Stock Markets
Martha Edith Bellini* and Antonio de-la-Torre-Gallegos**
This paper investigates systematic patterns of lead, coincidence or lag on
the prices of the most important commodities traded in the stock markets,
Gold and of Oil, taking of as basic chronologies that provided by the turning
points of the stock markets. The NBER approach is applied to identify
turning points in the American Stock Market (using S&P500 index), the
price of Gold and the price of Oil from January 1997 through June 2013.
The "G" program is used to analyze the delays between the turning points,
in order to classify the series according to the cyclical signal with respect to
the stock market into leading, lagged, or coincident. The results of the
cyclical classification show that the evolution of the price of gold is a
leading variable with respect to the S&P 500 when peaks and troughs are
separated at the time of performing the study. Hence, this variable can be
used when predicting the end of downward trend in the stock markets.
JEL Codes: G1, E32, G17, Q4,
1. Introduction
Empirical evidence and relevant facts disclose that financial and stock markets do not
follow a straight-line trend, but alternate between phases of a rising stock market and
economic expansion with other phases of a low market and/or recession, thereby forming
a series of peaks and troughs, which in turn determine this cyclical pattern. These cycles
trigger financial and stock market crises that affect financial markets and, and end up
affecting all economic sectors
The first authors to address the issue of business cycles were Burns and Mitchell (1946).
Business cycles have been analyzed since with Galbraith (1954) and Shiller (1989, 2005)
showing that business cycles are due to the irrational behaviour of investors, or “animal
spirit”. Siegel (1998) argues that the existence of cycles in the stock market reflects large
shifts in consensus perceptions of fundamentals and expectations of the future.
The existence of these cycles in the stock market contradicts the efficient market
hypothesis, based on the rationality of investors and the theory of random walk following
from Bachelier (1900) and Malkiel (1973). There are now many documented violations of
market efficiency. For instance, Banz (1981) shows that small stocks earn an abnormal
return compared to their risk. Hong et al. (2007) conclude their investigation by saying that
the industrial sector predicts stock market movements.
*Dra. Martha Edith Bellini, Department of Finance and Operation Management
University of Seville, Spain; Email: ebellini@us.es
**Dr. Antonio de-la-Torre-Gallegos, Department of Finance and Operation Management
University of Seville, Spain; Email atorre@us.es
2
Using monthly data from 1997:1 - 2013:06 we analyze the turning points of the US stock
market (S&P500), the price of Gold and the price of Oil, in order to investigate if the delays
of the turning points of the (S&P500) in relation to the variables studied can be used for
forecasting purposes and if the results of this investigation can be useful for long-term
investors in helping them to form profitable market-timing strategies. In a previous
research we studied the cyclical classification of several financial variables in relation to
the stock market and in this paper we selected two of the most significant variables that
showed to lead the stock markets, Bellini (2011).
This research applies the approach used by the National Bureau of Economic Research
(NBER) following Burns and Mitchell (1946) for the identification of turning points. The <G>
program from Abad and Quilis (1996) is used to analyze the delays between the turning
points, in order to classify the series according to the cyclical signal with respect to the
stock market into leading, lagged, or coincident.
The rest of the paper is organized as follows: In Section 2 we briefly present the literature
on stock markets cycles and cyclical classification of turning points. In Section 3 we
present the data and methodology followed in this investigation. In Section 4 we discuss
the results of our cyclical classification and section 5 provides some concluding remarks.
2. Literature Review
2.1 Identifying Cycles
There are two main approaches to locate the upward and downward phases of existing
cycles in an economic variable. The first one advocates a parametric specification of the
data generating process, where two different regimes are allowed, one that corresponds to
the expansions – and therefore contains some type of upward trend – and another one
that corresponds to the contractions and therefore contains a downward trend. Examples
of this approach are Goodwin (1993), Diebold and Rudebusch (1996) and Ramchand and
Susmel (1998). In particular, upward and downward phases are explicitly identified in
Maheu and McCurdy (2000) using parametric Markov-switching models.
The second approach takes a nonparametric perspective and, instead of fitting a fully
specified statistical data generating process, looks at the original data series in search for
the specific features of the cycle. That is, this procedure looks for periods of generalized
upward trend, which are identified with expansions, and periods of generalized downward
trend which are identified with contractions. The key feature of the analysis is the location
of turning points, peaks and troughs, in the series. These turning points determine the
different phases of the cycle, which can be subsequently analyzed. This method was first
applied by Bry and Boschan (1971) to the analysis of business cycles. It has since been
used by Watson (1994), Artis et al. (1997) and Harding and Pagan (2003) for business
cycles, and by Gómez Biscarri and Pérez de Gracia (2002), Kaminsky and Schmukler
(2003) and Pagan and Sossounov (2003) for stock market analysis. Candelon et al. (2008)
use nonparametric methods to measure the synchronization of bull and bear markets in
East Asian countries. Cyclical variations in stock returns are also widely reported in the
literature, see Coakley and Fuertes (2006), Perez-Quiros and Timmermann (2004).
One of the most used nonparametric method to recognize a cycle is the position taken by
the “classic cycle” or “business cycle” approach particularly in the studies of the National
Bureau of Economic Research (NBER) following Burns and Mitchell (1946).
3
This method involves the construction of a set of indicators of a cycle from the information
available on a continuous random variable yt. In this method, the presence of a cycle
(expansion and contraction) is indicated by the existence of turning points in the level
series without trend adjustments. The variable is designated as yt and assumes that it is
the log of the original series.
Since our aim is to extract and locate the turning point of the stock market the
nonparametric approach will be more suitable for this study as this method allows more
flexibility in analyzing some important features of the stock market cycles.
2.2. Locating Historical Turning Points in Stock Markets
Turning points are indentified by using the technique based on the NBER approach using
the “Busy Program” created by Fiorentini and Planas (2003)1. The NBER approach relies
on descriptive statistics and on the detection of turning points. It is based on a large
amount of empirical experience, as it has been developed since 1940’s. It has proved to
be well suited to the analysis of the US business cycle. Although it is a heuristic approach,
it is now a reference for macroeconomists (see for example Zarnowitz, 1992). In previous
paper we found that is more precise in locating the turning points of the FTSE100. Dunis et
al. (2011)
Many papers have analyzed the upward and downward trend following the algorithm
suggested by Bry and Boschan (1971) currently in use in stock market analysis: Pagan
and Sossounov (2003), Abad et al. (2000), and Gomez Biscarri and Perez de Gracia
(2004), among others.
2.3. Cyclical Classification
After analyzing the methods for cyclical classification applied to economic variables,
among which are found those that use delays between the turning points, (the crosscorrelation function, the spectral coherence function, and the dynamic factor model), it is
concluded that for the stock markets, and especially for trading strategies, the most
convenient method is that which analyses the delays between the turning points from the
use of the <G>2 program and, therefore, is the method utilized in this study.
The principal objective of program <G> is to classify a set of time series according to the
behaviour of its cyclical signal with respect to a given reference series into either leading,
lagged, coincident or acyclical variables. In this process, the cyclical signal of each series
is compared with that of the reference series, by computing the distance in months (delay)
between the turning points of each series. The calculation of the median value of all delays
enables the series to be assigned into any of the abovementioned categories.
1
We use the 'Busy' program to conduct our cyclical analysis of the S&P500 index. The program is
downloadable at : www.jrc.cec.eu.int/uasa/prj-busy.asp. Also by contacting: Christophe.planas@jrc.it.
2
Abad, A., Cristóbal, A y Quilis E.M. (2004): Programs for Cyclical Analysis, <F>, <G>,and <FDESC>,
Users guide.
4
3. The Methodology and Model
In this paper we identify the stock market turning points by locating the peaks and troughs
that signal a change in the trend using the NBER method, then the cyclical classification
are implemented in order to extend the knowledge about the financial markets and the
behaviour of the variables, to use the information for predictions. With this regard, the use
of leading indicators can be extremely helpful. For the cycle analysis the “Busy Program”
of Fiorentini and Planas (2003) is used and for the cyclical classification the <G> program
of Abad et Al. (2000).
3.1 The Data
The data used for this investigation is monthly data from American stock market (S&P500),
the price of Gold, the price of Oil and the Consumer Sentiment Index. The sample period
is 1997:1 - 2013:6 with 200 data points.
For the transformation of the data, the technique implemented relies in the first place on
second moment analysis. It is hence assumed that the series are second-order stationary,
with mean and auto-covariances that are finite and do not depend on time. Because most
economic time series do not satisfy these conditions, they need to be transformed.
Let Xit be a time series with sample length T, i.e. i=1,•••, N, .t=1, •••,T. Besides a logtransformation that serves at the cases where the series variance increases together with
the mean, according to the general expression:
∑
v
X
[1]
3.2 The NBER Approach
The NBER procedure starts with a detrending moving average; the method used for
detrending is the Hodrick-Prescott filter designed by Hodrick and Prescott (1997). The filter
is given by:
[2]
Where λ is the inverse signal to noise ratio, i.e. the ratio of the variance of the innovations
in the short-term component to the variance of the innovations in the long-term
component. For monthly series, typical values are λ=14400, see Hodrick and Prescott
(1997). The larger λ the smoother the long-term components, see also Harvey and Jaeger
(1993).
Secondly the stationary series is corrected for outliers. Outliers are identified as the points
that lie outside the
Z ,
Z
, where
denotes the sample mean of
the I-th series and
Z ) the sample standard deviation.
5
The turning points found in the reference series are produced together with descriptive
statistics such as average and median and details about the phases and length of the
cycle found are given. The transformed series together with the turning points are
presented in graphical format.
For monthly data, a 2x12 centered Moving Average (MA) is applied on the outliercorrected data in order to obtain the "first cycle" curve. A first set of potential turning points
is searched for in the 2x12 MA filtered series. The turning points are looked for in the
interval [t-nterm,t+nterm] where the default is nterm=5. A minimum phase length of
1.25*MQ periods from a peak (trough) to a peak (trough) is imposed, MQ denoting the
data periodicity of 12 for monthly series. The succession peak-trough is checked and
imposed if necessary.
3.3 The <G> program.
The identification of leading, coincident and lagged indicators for an economic system is
one of the main tasks of the cyclical analysis, with an origin dating back to the beginning of
the 20th century, with the NBER studies on the economy of the United States.
The procedures most commonly used consider that there is a special series acting as a
comparison standard, either for its economic relevance (e.g., the Gross Domestic Product)
either for its statistical properties (e.g., the Index of Industrial Production). The series to be
classified (xt) are related below one by one to the reference series (yt). In our study the
stock market (S&P500) will be the reference serie.
The procedures of cyclical classification can use the delays between the turning points: the
<G> procedure, the cross correlation function or the spectral coherence function. The first
two methods are defined in the time domain, while the third one is on the frequency
domain. For trading purposes is necessary to now the delays between the turning points,
so therefore the most convenient is the <G> procedure.
The cyclical classification based on the turning point tries to identify systematic patterns of
lead, coincidence or lag taking as basic chronologies that provided by the turning points of
the reference series (fy). In fact, if the series to be classified, xt, has its turning points with a
median delay3 ranging from –3 to 3 months from those of the reference series, it is
considered that both are coincident. If this median delay is lower (higher) than –3 (3)
months, it is considered that xt leads (lags) to yt.
A fourth possibility can also occur: that the turning points of xt are not consistent with those
of yt due to the lack of a common cycle between both series, usually due to a significant
difference between the main frequencies of both cycles.
Procedure <G> operates as follows: from the turning points of the reference series (fy) and
classified series (fx) identified by the method described in the above section, a
correspondence between them is established in three steps:
1. Each turning point of the series fy is associated with the nearest of fx,
2. Each turning point of the series fx is associated with the nearest of fy,
3. Unidirectional couplings are eliminated, retaining only the bi-directional ones.
3
The median is used because it is a robust estimator, so it is particularly useful in a setting of small samples
such as that commonly found in this type of analysis.
6
This relation is called double and shows the characteristic that two turning points of one
series cannot be associated with the same turning point of the other, so there can be
turning points without correspondence. If the number of turning points without
correspondence is high, it is considered that there is no cyclical relationship between the
turning points of x and y. This procedure of classification has been also programmed in
Pascal and is called <G> (Abad and Quilis, 1997).
The Ry and Rx ratios are a synthetic measure of the degree of conformity between two
series. That both are close to the unit is a condition necessary for a cyclical relation to
exist between the two series. If, on the contrary, both are close to zero, it is considered
that there is no cyclical relationship between the series or, in the terms of the program
<G>, the series x is cyclically unclassifiable in relation to series y (x <a> y). The cases
where Ry or Rx tend to zero (but not both simultaneously) suggest intermediate situations
where there can be some local, but no overall agreement, which is a sign of inconsistency.
In these cases, for more safety, it has been decided to consider also both series as
unclassifiable. The acceptance limits, Ly and Lx, are established a priori and, by default,
the program <G> assumes Ly=Lx=0.70.
4. Empirical Results: The Turning Points and the cyclical classifications.
4.1 The Turning Points using the NBER Approach
For the analysis we use the ‘Busy’ Program and the results of the turning points for the
American stock market (S&P500), the price of gold and the price of Oil in table 1 below.
The in-sample period analyzed is from 1997:1 through 2013:06.
S&P500:
Peak
Trough
Peak
Aug-87 Nov-87 May-90
Trough Peak
Trough Peak
Trough
Peak
Trough Peak
Trough
Oct-90 Jan-94 Jun-94 Jun-98 Aug-98 Aug-00 Sep-02 Oct-07 Feb-09
Peak
Trough
Apr-11
Sep-11
Gold:
Peak Trough Peak Trough Peak Trough Peak Trough Peak Trough
Peak Nov‐87 Aug‐89 Jan‐90 Feb‐93 Jan‐96 Aug‐99 Oct‐99 Mar‐01 Feb‐08 Oct‐08 Aug‐11
Oil:
Trough Peak
Trough
Peak
Trough
Peak
Trough
Peak
Trough
Peak
Trough Peak
Trough
Peak
Trough
Peak
Trough
Jul-86 Jul-87 Oct-88 Oct-90 Jan-92 Jun-92 Dec-93 Dec-96 Dec-98 Nov-00 Dec-01 Jul-06 Jan-07 Jun-08 Feb-09 Apr-11 Jun-12
Table 1: Results of NBER turning point analysis
4.2 Cyclical classification based on the turning points.
The dataset of the American stock market (S&P500), the price of gold, the price of Oil and
the Consumer Sentiment Index were analysed with the "G" program. The results are
presented on tables 2 and 3.
7
S&P 500
Date
Gold
Date
Delays (months)
S&P 500
Date
Gold
Date
Troughs
Troughs
Delays (months)
Peaks
Peaks
Jun‐98
‐
*
Aug‐98
Aug‐99
12
Aug‐00
Oct‐99
‐10
Sep‐02
Mar‐01
‐18
‐4
Oct‐07
Feb‐08
4
Feb‐09
Oct‐08
Apr‐11
Aug‐11
4
Sep‐11
Dec‐11
Dating for Cyclical Classification
*
Troughs vs Global Series Peaks vs Peaks
Troughs
Nº of turning points S&P 500
8
4
4
Nº of turning points Gold
6
3
3
Nº of paired turning points
6
3
3
Conformity ratio S&P 500
0.8
0.8
0.8
Conformity ratio Gold
1.0
1.0
1.0
Minimun limits of conformity
0.7
0.7
0.7
0.0
Coincident
4.0
Laddged
‐4.0
Leading
Median delay
Cyclical Classification Gold vs S&P 500
Table 2: Results of Cyclical classification for the gold
S&P 500
Date
Oil
Date
Delays (months)
S&P 500
Date
Oil
Date
Troughs
Troughs
Delays (months)
Peaks
Peaks
jun‐98
ene‐97
‐17
ago‐98
dic‐98
4
ago‐00
nov‐00
3
sep‐02
dic‐01
‐9
‐
jul‐06
*
‐
ene‐07
*
oct‐07
abr‐11
jun‐08
abr‐11
8
0
feb‐09
sep‐11
feb‐09
jun‐12
0
9
Dating for Cyclical Classification
Global Series
Peaks Troughs Nº of turning points S&P 500
8
4
4
Nº of turning points Oil
10
5
5
Nº of paired turning points
8
4
4
Conformity ratio S&P 500
1.0
1.0
1.0
Conformity ratio Oil
0.8
0.8
0.8
Minimun limits of conformity
0.7
0.7
0.7
Median delay
1.5
1.5
2.0
Coincident
Coincident
Coincident
Cyclical Classification Oil vs S&P 500
Table 3: Results of Cyclical classification for the oil
The prices of gold and the oil are coincident variables with respect to the S&P 500 when
the series is analysed as a whole. However, if the peaks and troughs are separated at the
time of performing the study, it can be observed that the price of the gold leads the troughs
of the S&P 500. Hence, this might be the variable that could provide a sufficiently early
prediction of the end of the downward trends and, therefore, be valid to open long-term
positions in the trading systems.
5. Concluding Remarks
The results of the cyclical analysis using the NBER approach and the cyclical classification
using the "G" program show that from the two financial variables analysed, the price of
gold is the only leading variable with respect to the S&P 500 when the analysis of the
peaks and troughs are separated at the time of performing the study. The prices of gold
and the oil are coincident variables with respect to the S&P 500 when the series is
analysed as a whole.
8
As an overall conclusion, only the price of gold has behaved as a leading variable, and
hence this might be the only variable that could provide a sufficiently early prediction of the
end of the downward trends. It can be confirmed that the analysis of the delays between
the turning points of some commodities (the price of gold and price of oil) in relation to the
stock market can be of great use facilitating the achievement of higher yields.
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