On kendall's tau as a test of trend in time series data

Abstract

Abstract Kendall's tau is often used to detect the presence of trend in environmental time series data. Assuming stationarity, a general expression for the variance of the associated S score is derived. The results are specialized to the cases of MA(1) and MA(2). Asymptotic normality of tau is established. It is shown that the variance of tau is strongly affected by the assumption of statistical dependence. A seasonal model with non‐zero correlations between successive seasons and years is considered. Simulation results indicate that the effects of departures from distributional assumptions are less important when compared to the effects of departures from the independence assumption.