Global autocorrelation test based on the Monte Carlo method and impacts of eliminating nonstationary components on the global autocorrelation test

Autocorrelation and non-stationarity are always concerned in analysis of meteorological and hydrological time series. Current commonly used methods, such as the Box-Pierce (BP) test and Ljung-Box (LB) test, always preset the maximum order for the autocorrelation significance test without considering the existence of high-order autocorrelation coefficient(s), and also neglect a fact that the sum of sample autocorrelation function is a constant value. Moreover, the impacts of autocorrelation on the significance test of nonstationary components of sample time series have drawn much attention, but less attention is paid to the impacts of eliminating nonstationary components on the global autocorrelation significance test. These issues are addressed in the paper. Based on the Monte Carlo method, a global autocorrelation test method, the quadratic sum (QS) test, is presented for judging the existence of high-order autocorrelation coefficient(s) of a sample time series. Besides, two nonparametric trend estimators (nonlinear and linear trend estimators) are employed to investigate the impacts of eliminating nonstationary components on the global autocorrelation test. The results show that (i) the QS test method is more robust than the BP test and LB test in verifying the existence of significant high-order autocorrelation coefficient(s); and (ii) eliminating a linear trend has less damage on the original global autocorrelation structure of sample time series by comparing with eliminating a nonlinear trend. Therefore, it is recommended to initially eliminate the linear trend from a sample time series, and then judge the existence of high-order autocorrelation coefficients of the time series based on the QS test.