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
Abstract:
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.