On trend detection

A main obstacle to trend detection in time series occurs when they are autocorrelated. By reducing the effective sample size of a series, autocorrelation leads to decreased trend significance. Numerous recipes attempt to mitigate the effect of autocorrelation, either by adjusting for the reduced effective sample size or by removing the autocorrelated components of a series. This short note deals with the latter, also called prewhitening (PW). It is known that removal of autocorrelation also removes part of the trend, which may affect the signal-to-noise ratio. Two popular methods have dealt with this problem, the trend-free prewhitening (TFPW) and the iterative prewhitening. Although it is generally accepted that both methods reduce the adverse effects of PW on the trend magnitude, corresponding effects on statistical significance have not been clearly stated for TFPW. Using a Monte Carlo approach, it is demonstrated that both methods entail quite different Type-I error rates. The iterative prewhitening produces rates that are generally close to the nominal significance level. The TFPW, however, shows very high Type-I error rates with increasing autocorrelation. The corresponding rate of false trend detections is unacceptable for applications, so that published trends based on TFPW need to be reassessed.