Bivariate and higher-order terms in models of international equity returns

Nonsynchronous measurement induces significant higher-order auto and serial cross correlations in observed bivariate returns and squared returns to international equity indices. In order to investigate the statistical and economic significance of bivariate and higher-order terms in conditional models of international equity returns, we fit a VMA(2)-EGARCH(2,2) model with normal errors and a constant conditional correlation using MSCI index pairs for Japan, the UK and the USA. First-order univariate and bivariate conditional mean and volatility terms are statistically significant in each series. Second-order own- and cross-volatility terms also are significant, although second-order conditional mean terms are not. We investigate the economic significance of bivariate and second-order terms by comparing the return and volatility predictions of various models using out-of-sample regressions of returns or squared returns on conditional means or volatilities. Bivariate terms significantly improve return prediction in three of six series and volatility prediction in one of six series. Higher-order conditional volatility terms do not improve predictions of returns and squared returns despite the fact that they are statistically significant in these series. We conclude that it is important to include cross-effects, but not higher-order effects, when modelling conditional returns to international stock market indices.