Checking the Independence of Two Covariance-Stationary Time Series: A Univariate Residual Cross-Correlation Approach

A two-stage method is proposed for investigating the independence of two covariance-stationary time series. It involves, first, fitting univariate models to each of the series, and then cross-correlating the two residual series thereby obtained. The asymptotic distribution of such a set of lagged residual cross-correlations is established to be of a very simple form under the null hypothesis of the two series' independence. A Monte Carlo study verifies the applicability of this distribution for series of length N = 50, 100, and 200. An attendant chi-square test statistic is discussed.