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Journal of Empirical Finance 7 2000 155–172 www.elsevier.comrlocatereconbase
Visualizing time-varying correlations across stock markets
Patrick J.F. Groenen
a,
, Philip Hans Franses
b
a
Data Theory Group, Department of Education, Leiden UniÕersity, P.O. Box 9555, 2300 RB Leiden, Netherlands
b
Econometric Institute, Erasmus UniÕersity Rotterdam, Rotterdam, Netherlands Accepted 9 May 2000
Abstract
We propose a graphical method to visualize possible time-varying correlations between stock market returns. The method can be useful for observing stable or emerging clusters of
stock markets with similar behavior. The graphs, which originate from applying multidi- Ž
. mensional scaling techniques MDS , may also guide the construction of multivariate
econometric models. We illustrate our method for the returns and absolute returns of 13 important stock markets. q 2000 Elsevier Science B.V. All rights reserved.
Keywords: Multidimensional scaling; Stock market returns; Time-varying correlations
1. Introduction and motivation
In this paper we propose a basically graphical descriptive method, which can yield insights into possible similarities across stock markets. The empirical results
from our method can be helpful in guiding the design of statistical models, and these can be used to test hypotheses of interest. Additionally, our method can
perhaps lead to the postulation of new hypotheses.
There are economic and statistical motivations why one would obtain insights into the correlation structure of international stock markets, while allowing for the
possibility that this structure varies over time. An important economic motivation
Corresponding author. Tel.: q31-71-527-3826; fax: q31-71-527-3865. Ž
. E-mail address: groenenfsw.leidenuniv.nl P.J.F. Groenen .
0927-5398r00r- see front matter q 2000 Elsevier Science B.V. All rights reserved. Ž
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concerns the potential integration of international stock markets. For example, a relevant question is whether there is a single world factor that governs country-
specific stock market behavior. Related to this, another interesting issue concerns the extent to which an emerging market can still be called emerging, where it is
assumed that an emerging market displays different dynamic patterns over time
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than other markets do. Bekaert and Harvey 1995 and Bekaert et al. 1998 propose several relevant econometric methods for this issue. Our method can be
seen as an additional tool to their formal methods, or perhaps as a graphical tool that can precede the analysis. Another economic motivation concerns the possibil-
ity of including information on changing correlations to design more optimal portfolios.
The statistical motivations are mainly given by the fact that multivariate models for stock market returns and volatility contain a substantial number of parameters,
Ž .
see Kroner and Ng 1998 for a recent survey. The multivariate models developed Ž
. Ž
. Ž
. in Bollerslev 1990 , Engle and Susmel 1993 and Engle et al. 1990 need quite a
number of parameter restrictions to enable estimation. Even though Ledoit and Ž
. Santa-Clara 1998 show that unconstrained multivariate models for volatility can
be estimated for large numbers of assets, it may still be useful to visualize correlations in order to suggest some potentially plausible parameter restrictions.
Indeed, as the number of variables does not necessarily limit the application of our method, it can, in principle, be used to suggest parsimonious model structures.
This may be enhanced by the possible detection of a few underlying factors.
As an example of the relevance of our exercise below, consider the following. A practically tractable multivariate GARCH model imposes constant conditional
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correlations across volatility, see Bollerslev 1990 . Our empirical results for 13 international stock markets in Section 3 will show that this may not be a plausible
assumption, at least not for these series. In fact, we find that there appears to be three clusters, which tend to have constant correlation in the last few years, of our
sample only. We also observe that large stock market crashes seem to correspond with changing correlation structures.
The outline of our paper is as follows. In Section 2, we give the basics of the Ž
. multidimensional scaling MDS technique, which is at the core of our empirical
method and discuss the details that are relevant for our specific application. In Section 3, we apply our method for daily data on 13 stock markets, including
major American, Asian, and European stock markets. We consider daily returns
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and volatility measured as absolute returns . In Section 4, we conclude our paper with some final remarks and potential topics for further research.
2. On MDS
