Linear Trend Detection in Serially Dependent Hydrometeorological Data Based on a Variance Correction Spearman Rho Method

Abstract

Hydrometeorological data are commonly serially dependent and thereby deviate from the assumption of independence that underlies the Spearman rho trend test. The presence of autocorrelation will influence the significance of observed trends. Specifically, the positive autocorrelation inflates Type I errors, while it deflates the power of trend detection in some cases. To address this issue, we derive a theoretical formula and recommend an appropriate empirical formula to calculate the rho variance of dependent series. The proposed procedure of the variance correction for the Spearman rho method is capable of mitigating the effect of autocorrelation on both, Type I error and power of the test. Similar to the Block Bootstrap method, it has the advantage that it does not require an initial knowledge of the autocorrelation structure or modification of the series. In comparison, the capability of the Pre-Whitening method is sensitive to model misspecification if the series are whitened by a parametric autocorrelation model. The Trend-Free Pre-Whitening method tends to lead to an overestimation of the statistical significance of trends, similar to the original Spearman rho test. The results of the study emphasize the importance of selecting a reliable method for trend detection in serially dependent data.

Statistical Uncertainty in Hydrometeorological Trend Analyses

“…Moreover, whereas MK and CRD apply correction for the influence of ties in the computation of the test statistic variance, the SMR corrects for ties in the calculation of the test statistic itself. When dealing with the influence of short-term persistence, the SMR uses an exact expression for the variance of the test statistic under the assumption of multivariate Gaussian dependence [18] or theoretical formula for variance correction [22]. Furthermore, serial correlation can be tackled by: prewhitening [23][24][25], resampling techniques in terms of sieve-bootstrap [26], block bootstrap [27] or phase randomisation [28], and variance correction using either rank-based empirical formula [29] or direct application of the effective sample size [30].…”

“…Furthermore, prewhitening procedures based on various approaches including trendfree prewhitening [25], simultaneous estimation of trend slope and autocorrelation coefficient [45], variance correction prewhitening [24], and modified trend-free prewhitening [46] were also applied. For the SMR, the variance inflation factors based on the long-term persistence [18], Gaussian dependence proposed by [18], and the theoretical formula based on the effective sample size [22] analogous with the procedure of [30] for the MK were applied. For the CRD, variance correction approach based on short-term persistence [12] as well as that for the long-term persistence (see Appendix B of this paper) were applied.…”

Statistical Analysis for Assessing Randomness, Shift and Trend in Rainfall Time Series under Climate Variability and Change: Case of Senegal

“…So, in some degrees, correlation between observations in Spearman's rho and Kendall's tau tests for independence assessment is associated to presence of trend in time series [23] [24] [25]. Hence, null hypothesis of randomness H 0 is tested against alternative hypothesis H 1 .…”

Multidecadal trend analysis of aerosol radiative properties at a global scale

“…The MK test is designed for serially independent data and is consequently influenced by autocorrelation in the time series leading to inflated type I error; that is, there is increased probability of rejecting the no-trend hypothesis (i.e., a false positive). Several correction schemes for the MK test were proposed to correctly handle autocorrelated datasets and the problems induced by autocorrelation and its various corrections have been clearly described (Wang and 25 Swail, 2001;Yue et al, 2002;Bayazit and Önöz, 2007;Blain, 2013;Wang et al, 2015). A new method has been used for this study that tends to minimize the type I and II error (type II error is non-rejection of a false null hypothesis, i.e., a false negative) as well as the modification of the slope due to pre-whitening procedures by the application of three prewhitening methods (Collaud Coen et al, in preparation).…”