Empirical Framework for Univariate Modeling
We begin our analysis by modeling the time series of excess country returns
net of the world-market portfolio as a univariate GARCH process.
Australia 2 January 1980–31 December 1997 779 3572
Austria 20 November 1987–31 December 1997 1162 1334
Belgium 2 January 1990–31 December 1997 941 1037
Canada 2 January 1973–31 December 1997 2740 3516
Chile 2 January 1987–31 December 1997 879 1741
Denmark 10 December 1979–31 December 1997 2476 2037
Finland 2 January 1987–31 December 1997 333 2424
France 9 July 1987–31 December 1997 330 2270
Germany 21 November 1977–31 December 1997 3215 1771
Japan 4 January 1980–31 December 1997 2098 2298
Hong Kong 2 January 1973–31 December 1997 3263 2888
Hungary 2 January 1991–31 December 1997 1056 674
Israel 2 January 1992–31 December 1997 928 527
Italy 2 January 1973–31 December 1997 5507 780
Korea 3 January 1990–31 December 1997 1540 398
Malaysia 2 January 1980–31 December 1997 3902 508
Netherlands 3 January 1983–31 December 1997 1402 2313
Norway 3 January 1983–31 December 1997 2418 1333
Portugal 1 January 1993–31 December 1997 853 376
South Africa 10 April 1985–31 December 1997 1136 1891
Spain 6 January 1987–31 December 1997 1238 1501
Sweden 2 January 1986–31 December 1997 311 2694
Switzerland 1 July 1988–31 December 1997 590 1792
United Kingdom 2 January 1973–31 December 1997 2871 3485
United States 2 January 1973–31 December 1997 2340 3967
This framework is parsimonious, which allowed us to capture many of
the salient features of the data, and to partially account for movements
in the world market in a model with relatively few parameters. Later, we
would estimate a multivariate GARCH model that would allow us a richer
model of the joint dynamics of country-specific and world-market returns.
Following Pagan and Schwert (1990) and Engle and Ng (1993), the
first step in our univariate GARCH analysis was to remove from the time
series any predictability associated with lagged returns or day-of-the-week
effects. For each country, the following regression was estimated:
where Rt is the daily return on the country’s stock index and RWt is the
daily return on the World Market Index on day t, RWt1 is the lagged return on the World Market Index, and DAYj are day-of-the-week dummies
for Tuesday through Friday.
We used the excess return relative to the World Market Index as our
dependent variable and the lagged World Market Index return as an independent
variable in an effort to remove the effect of worldwide price
movements on volatility.6 It should be noted that because of differences
in time zones, different markets line up differently with the world-market
return. This makes it difficult to compare directly the coefficients of the
first-stage regression. For example, if the U.S. market is influenced by
Asian markets, this will be reflected through the contemporaneous market
return on the left-hand side of the regression equation. On the other
hand, if the Asian markets are influenced by the US, this will be reflected
through the lagged market portfolio.
