Testing for Relationships between Time Series

The usual procedures for testing the significance of sample correlations between pairs of independently normally distributed series are not appropriate for testing sample correlations between pairs of autocorrelated series. We present sampling evidence supporting our hypothesis that the distributions of sample correlations between pairs of unrelated first-order Markov series conditional on the first lag sample autocorrelations of the series correlated are independent of the population first lag autocorrelations of these series. Based on this evidence, a new test of significance for correlations between autocorrelated series is proposed, which, although treating them as first-order Markov series, does not depend on the generally unknown generating properties of the series.

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