Kendall's tau for autocorrelation

Thomas S. FERGUSON, Christian GENEST and Marc HALLIN

University of California at Los Angeles, Universitè Laval and Universitè libre de Bruxelles


The authors show how Kendall's tau can be adapted to test against serial dependence in a univariate time series context. They provide formulas for the mean and variance of circular and non-circular versions of this statistic and they prove its asymptotic normality under the hypothesis of independence. They present also a Monte Carlo study comparing the power and size of a test based on Kendall's tau to that of competing procedures based on alternative parametric and nonparametric measures of serial dependence. In particular, their simulations indicate that Kendall's tau outperforms Spearman's rho in detecting first-order autoregressive dependence, despite the fact that these two statistics are asymptotically equivalent under the null hypothesis.