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.

自相关和非平稳性始终是气象和水文时间序列分析中关注的问题。当前常用的方法，例如Box-Pierce（BP）测试和Ljung-Box（LB）测试，总是在不考虑存在高阶自相关系数的情况下预设自相关显着性检验的最大阶数，并且忽略了样本自相关函数之和为常数的事实。此外，自相关对样本时间序列非平稳分量显着性检验的影响已引起广泛关注，但消除非平稳分量对全局自相关显着性检验的影响关注较少。本文解决了这些问题。基于Monte Carlo方法（一种全局自相关测试方法），提出了二次和（QS）检验来判断样本时间序列的高阶自相关系数的存在。此外，还采用了两个非参数趋势估计器（非线性和线性趋势估计器）来研究消除非平稳分量对全局自相关检验的影响。结果表明：（i）在验证存在显着的高阶自相关系数时，QS测试方法比BP测试和LB测试更可靠；（ii）与消除非线性趋势相比，消除线性趋势对样本时间序列的原始全局自相关结构的损害较小。因此，建议首先从采样时间序列中消除线性趋势，