Some Studies On The Non-stationarity Analysis Of Time Series

Affected by climate change and human activities, variations have occurred in the hydrological system. This paper takes the hydrological processes as the research back-ground and investigates the non-stationarity of time series in terms of the non-stationary form of the time series, non-parametric detection methods and time-varying parametric statistical model based on three-parameter gamma distribution.Chapter2investigates the ability of the widely used Pettitt method for detecting change point. The ability of the Pettitt method for detecting change point is defined as the success rate in simulation experiments, and the relationships between the ability and various influence factors including the pre-assigned significance level, the sample size, the magnitude of a shift, the change point position, the distribution type and the distribution parameters, are investigated. Results indicate that the Pettitt method is not distribution-free and sensitive to skewed distributions. The study case corroborates the simulation results which provide users a new reference.In Chapter3, after trend analysis methods at home and abroad are summarized, a new nonparametric temporal change analysis approach is proposed based on data char-acteristics to avoid the ignoring of data characteristics and change point information in the non-stationarity analysis of time series. The application of the new approach consists of data characteristics analysis, temporal change analysis, and the result in-terpretation. Proper statistical methods are chosen on the basis of the characteristics of the studied data. The approach of carrying out change point analysis before the trend analysis can avoid the shortcoming of ignoring the change point. Study case in-dicates the proposed method is both reliable and reasonable for the exploration of the non-stationarity in hydrological time series.Chapter4studies the method to distinguish change point from trend. Change point and linear trend are studied as two typical forms of non-stationarity. The detection success rate of some test methods are investigated using stochastic simulations which confirms that it is difficult to distinguish change point from trend component. After the detection success rate of an introduced indicator detection method is investigated, study case shows the necessity and feasibility of distinguishing the two components.In Chapter5, with the known position of the change point, time-varying parame-ter statistical model is constructed based on the three-parameter gamma distribution. Based on cross-entropy, an approximate maximum likelihood method is proposed for the estimation of the model parameters. Statistical tools such as AIC and Q-Q plot are used in the model selection and model diagnostic checking, respectively. Study case indicates the rationality and feasibility of the proposed model.In Chapter6, after the dissertation is summarized, the insufficient of the study and some research prospects are provided.