Quantification of Long-Range Dependence in Hydroclimatic Time Series: A Method-Comparison Study

Abstract Accurate evaluation of the long-range dependence in hydroclimatic time series is important for understanding its inherent characteristics. However, the reliability of its evaluation may be questioned, since different methods may yield various outcomes. In this study, we evaluate the performances of seven widely used methods for estimating long-range dependence: absolute moment estimation, difference variance estimation, residuals variance estimation, rescaled range estimation, periodogram estimation, wavelet estimation (WLE), and discrete second derivative estimation (DSDE). We examine the influences of six major factors: data length, mean value, three nonstationary components (trend, jump, and periodicity), and one stationary component (short-range dependence). Results from the Monte Carlo experiments show that WLE and DSDE have greater credibility than the other five methods. They also reveal that data length, as well as stationary and nonstationary components, have notable influences on the evaluation of long-range dependence. Following it, we use the WLE and DSDE methods to evaluate the long-range dependence of precipitation during 1961–2015 on the Tibetan Plateau. The results indicate that the precipitation variability mirrors the long-range dependence of the Indian summer monsoon but with obvious spatial difference. This result is consistent with the observations made by previous studies, further confirming the superiority of the WLE and DSDE methods. The outcomes from this study have important implications for modeling and prediction of hydroclimatic time series.