Johan Knif, Swedish School of Economics and Business Administration, P.O.Box 287, FIN-65101 Vaasa Finland

Seppo Pynnonen*, School of Business Studies, University of Vaasa, P.O.Box 700, FIN-65101 Vaasa Finland

This paper analyzes volatility structures and the presence of common volatility components in the stock markets of Asian-Pacific, Europe and North America using close-to-close daily returns in local currencies. The return series are filtered before volatility modeling in order to remove first order autocorrelations. Furthermore, the consequences of nonsynchroneity in the opening hours of the markets around the globe are carefully taken into account. The results indicate that an ARCH-effect is present in all the markets. However, only a few pairs of markets seem to share common volatility. USA is present in most of these pairs. Of the European markets, only France and the small Nordic markets seem to share a common volatility process with USA. It seems that the small markets follow the volatility process generated in US. Furthermore, a common time-varying volatility process seems to be present in Canada and US. In addition, Hong Kong seems to share a common volatility with US. Analysis of weekly data suggests that common volatility is at most a regional feature.

The analysis utilizes daily close-to-close index returns from eleven markets including the stock exchanges in New York, Toronto, Tokyo, Hong Kong, London, Frankfurt, Zurich, Paris, Copenhagen, Stockholm, Oslo and Helsinki. The sample series starts on September 7, 1991 and ends November 10, 1997. The data is obtained from Global Financial Data Base. New York and Toronto floor trading hours have two hours overlap with London, one and half an hour overlap with Paris, Stockholm and Zurich, and half an hour overlap with Oslo and Helsinki. Hong Kong and Tokyo do not overlap with New York, Toronto or the European stock exchanges. The European exchanges are essentially open at the same time.

Descriptive statistics show the sample period is characterized by a small positive mean daily returns between 0.04–0.06 percentages for USA, Canada, UK, France, Denmark and Norway. Hong Kong, Switzerland, Sweden and Finland have had returns around 0.08 percentage and Japan has had a slight negative average return of –0.01 percentage. Excess kurtosis is obvious in all series. All distributions, except Finland, Norway and France seem to be skewed, too. Sweden, UK and Japan are positively skewed, and the rest (Denmark, Germany, Switzerland, USA, Canada and Hon Kong) are negatively.

Analyzing common volatility in return innovations on daily basis using close-to close data causes a problem with nonsychroneity of opening hours. If the trading hours do not coincide it may cause dependencies that show spurious information transmission. Because of the close-to-close daily data there is perfect nonsynchroneity between Asian-Pacific and the other markets and an almost perfect nonsynchroneity between European and North American markets. The European markets are trading almost simultaneously. In determining return innovations, we take account of the different trading hours by allowing the same day returns of Asian Pacific and European markets to appear in the North American regression equations. Similarly, we allow the Asian Pacific same day returns to appear in the European regression equations. The rationale is that the new information processed in the earlier markets are fully available as the latter markets open later on during the same day as the earlier markets are essentially already closed.

We analyze the common volatility pattern in the spirit of Engle and Kozicki (1993) and Engle and Susmel (1993) (see also Arshanapalli, Doukas and Lang 1997). The first step is test for an ARCH-effect in each single series. As autocorrelation in the series will generate autocorrelation in the squared series (volatility entities), we account for the first order correlations using a structural VAR-model. There is strong evidence that Sweden and Norway are cointegrated with a trend in the cointegration space. This effect was also observed in a different (and shorter) data set, see Knif and Pynnonen (1997). Therefore, we removed also this effect from the return series of these two particular individual markets. No other clear evidence of cointegration was found. The fitted structural VAR model contains five lags of all return series of the European markets and the same day return of Japan and Hong Kong. To the regression models for Norway and Sweden the lagged cointegration residual was also added. For Canada and US the same day returns of the European markets were included. For Japan and Hong Kong only lagged returns were used as regressors. In this way we have eliminated the autocorrelation bias in the ARCH-testing.

The general result in the common ARCH-effect test is that only few markets seem to share a common time-varying volatility process. USA is present in almost all of these pairs. An interesting feature is that from the European markets, with the exception of France, only the small Nordic markets seem to share a common volatility process with USA. The common volatility process hypothesis is only borderline accepted for Denmark, Norway and Sweden. The results indicate that especially the small markets are sensitive to shocks occurring on the world leading US market. Consequently, instead of talking about a common volatility process, one rather can say that the small markets are following the volatility process determined by the US markets.

In North America, the common time-varying volatility hypothesis is accepted as well between Canada and US. In the Asian-Pacific, also Hong Kong seems to have a common volatility process with US.

Altogether, these empirical results differ from those of Engle and Susmel (1993) and also from those of Arshanapalli et al. (1997). However, Engle and Susmel used weekly data and Arshanapalli et al. utilized daily data for only one year; 1993. Our data set consists of daily returns covering nearly seven years. Hence, with the increased number of observations smaller deviations from the null hypothesis, common ARCH-feature, is expected to emerge.

To make the results better comparable we run weekly analysis as well. The univariate ARCH results change to some extends from the daily case, where ARCH-effect was inferred to be present in each series. Now Sweden, Denmark, France, USA and Canada do not show univariate ARCH. Augmenting the univariate information set by other series, ARCH-effect can be inferred to be present additionally in France and possibly in Sweden, Denmark and Canada. Still there is no sign of ARCH in USA.

These preliminary results suggest that one obvious group for potential common ARCH effect might be the big European markets of Great Britain, Germany, France and Switzerland because, at least after augmenting the information set each series seems to have ARCH effect. A second European group might be the small Nordic countries of Denmark, Finland Norway and Sweden. North America and Pacific Asian areas form their own two natural groups on the basis of geographical reasons. Using these groupings as the basis, we test the existence of a common ARCH effect between the markets within the groups if either both series have a univatiate ARCH or multivariate ARCH after augmenting the information set by the test pair. Furthermore, we test the existence of an ARCH beyond geographical groups between those series that have multivariate ARCH after augmenting the information set by the test pair. The results strongly indicate that there is no common volatility process between the small Nordic markets, although the null hypothesis of common volatility between Finland and Norway would be accepted even at a ten percent level. Norway, however, does not share a common volatility process with Great Britain, but Finland does. Consequently because of the equivalence relation property Norway should share a common volatility process with Great Britain as well. Because this is not the case, we can rather infer as in the daily case that these small countries may at most follow the volatility behavior of some of the larger European markets. This partially supports the general result found in the earlier daily analysis.

Among the big European markets, France, Germany, Great Britain and Switzerland, there is strong evidence of a common ARCH feature. In addition, Japan and Hon Kong seem to share a common volatility process, but USA and Canada do not because there is no sign of existence of an ARCH feature at weekly level in the USA series. The cross-continental tests indicate that only Canada and Great Britain might share a common ARCH process.

As a summary the results strongly support the idea found in Engle and Susmel (1993) and Archanapalli et al. (1997), that if there is a common volatility process it tends to be a regional one.