A new prewhitening approach for trend analysis in the autocorrelated time series.

In combination with Sen's slope, the non-parametric Mann–Kendall (MK) test is one of the most often used statistical techniques for determining a time series' trends. A serially uncorrelated time series is required for the MK test since the autocorrelation in the dataset seriously affects the type 1 and type 2 errors and reduces the performance of the MK test in detecting the statically significant trend. To mitigate this problem, numerous prewhitening techniques (PW, PW-Cor, TFPW-Y, TFPW-WS, VCTFPW; See Collaud Coen et al., 2020) have been developed that effectively reduce lag-1 autocorrelation. In this work, we have proposed a new prewhitening scheme (named as TFPW-Mod) and compared it with previous prewhitening schemes by constructing 5000 linear-trend superimposed (β) AR1 time series with lag-1 autocorrelation (ρ₁) using Monte Carlo simulation. We found that the new prewhitening approach keeps a very good balance between maintaining a low number of type 1 and type 2 errors. The results show that the occurrence of both types of errors largely depends on the length of the time series, with longer periods leading to a strong reduction of errors and to lower bias in the trend slope estimation. For weaker trends and/or the low number of samples, TFPW-Mod couldn’t restore the power of test. However, for a strong trend, this method yields the strongest power, almost independent of the lag-1 autocorrelation. The slope estimation of TFPW-Mod is robust for lower/Medium ρ₁, but significantly deviates from the original trend for highly correlated time series. In most cases, β_TFPW-Mod has lower RMSEs than β_VCTFPW, and leads to the unbiased slope estimation with better accuracy.