Enhancing the effectiveness of prewhitening in trend analysis of hydrologic data

SummaryPrewhitening of hydrologic as well as other types of natural time series has been suggested in the literature to eliminate the adverse effect of autocorrelation on the results of trend tests. It has been suggested in a recent study that prewhitening is not recommended when a true trend exists in the data. When prewhitening is applied, there has also been a debate on whether or not to remove an apparent trend before estimating the autocorrelation parameter ρ to ensure effective prewhitening. This is because while failing to remove an apparent trend before estimating ρ results in loss of power due to overestimation of ρ when a true trend exists in the data, it is also true that removing an apparent trend before estimating ρ results in loss of significance due to underestimation of ρ when no trend exists in the data. In this study, the applicability of prewhitening in the possible presence of a true trend is first established. It is then shown that simultaneous estimation of the trend slope and the autocorrelation coefficient, followed by correction of bias in the correlation coefficient largely eliminates the under/over-estimation of ρ within the limits of sampling variations, thus greatly enhancing the effectiveness of prewhitening. It is also shown that careful inference about the correlation model is critical for effective prewhitening. A comparison between the results obtained with and without bias correction is presented for a case study of trends in riverflow series from different parts of the world. The results emphasize the importance of bias correction in small samples, as well as the importance of careful choice of a serial correlation model for the data, especially in the case of long time series.