Tests for Non-Correlation of Two Multivariate Time Series: A Nonparametric Approach

Most of the recent results on tests for non-correlation between two time series are based on the residual serial cross-correlation matrices resulting from appropriate modelling of the two series. However in the stationary case, test procedures can be defined from the serial cross-correlation of the original series, avoiding therefore the modelling stage. This paper aims at describing two such tests that take into account a finite number of lagged cross-correlations. The first one that is essentially valid for Gaussian time series makes use of a procedure for estimating the covariance structure of serial correlations described in Mélard, Paesmans and Roy (1991). The second one that is valid for a general class of mixing processes is based on the property that the cross-covariance at a given lag between two stationary processes is in fact the mean of the product of the two processes, the second one being lagged appropriately. For both approaches, the asymptotic distributions of the test statistics are derived under the null hypothesis of non-correlation between the two series. The level and power of the proposed tests are studied by simulation in finite samples and an example is presented.