Consistent detection of a monotonic trend superposed on a stationary time series

Abstract

Consider a time series made up of a signal and a stationary autocorrelated error series. A statistic is proposed for examining the hypothesis that the signal term is constant versus the hypothesis that it is monotonic in time. The statistic is the ratio of a linear combination of the time series values, with coefficients introduced by Abelson & Tukey (1963), to an estimate of the standard error of the linear combination. The statistic has asymptotic power 1 for a broad class of monotonic alternatives. The procedure is illustrated for the series of river heights at a location on the Rio Negro in Brazil where there is concern that the height is rising due to deforestation of the Amazon Basin. The significance level obtained is 0·025