Common Persistence in Conditional Variances

A common finding in many of the recent empirical studies with the ARCH class of models applied to high frequency financial data concerns the apparent persistence of shocks for forecast of the future conditional variances. It is likely that several different variables share this same implied long-run component, however. In that situation, the variables are defined to be copersistent in variance. Conditions for copersistence to occur in the linear multivariate GARCH model are presented. These conditions parallel the conditions for linear cointegration in the mean. A simple empirical example with foreign exchange rate data illustrates the ideas. Copyright 1993 by The Econometric Society.