Distribution of the cross-correlations of squared residuals in ARIMA models

The distribution of the cross‐correlations of squared residuals from Box‐Jenkins models is considered in very general conditions, and the asymptotic distribution is derived. A test for a lagged relationship in volatility for economic time series under instantaneous causality is proposed, and its empirical behaviour is studied. An example involving the international stock market's volatility is studied, and an interesting result is observed. Copyright © 1996 Statistical Society of Canada.