Monitoring And Detecting Change-points In Several Classes Of Time Series Models

Time series models are established based on the observed time series. In this thesis, we discuss three classes of time series models: random coefficient autoregressive(RCA) model, generalized autoregressive conditional heteroskedasticity(GARCH) model and logistic regression model, the time series models mentioned above are one-dimensional data models, panel data are two-dimensional data sets with time series data and cross-sectional data. Time series and panel data models are important in the study of econometrics. In time series and panel data analysis, monitor and test whether there are change-points in the model parameters have great importance to establish the model and analyze the data correctly. This thesis investigates the change-points monitoring and detection in RCA(p) models, GARCH(p, q) models, Logistic regression models and Panel data models. The main research results and innovation points of the thesis are as follows:(1) A fluctuation monitoring statistic is proposed to monitor parameter changes in RCA(p) models, which first extends parameter changes monitoring to RCA(p) models. The asymptotic distributions of our test statistics are derived under the null hypothesis and the consistency are proved under the alternative hypothesis. Simulation results show that our procedure can achieve good performance when choose appropriate boundary function. Simulation results and empirical application demonstrate the effectiveness of the proposed method.(2) The Kolmogorov-Smirnov and empirical characteristic function statistics are given to monitor the distributional changes of squared residuals in GARCH(p, q) models. The asymptotic distributions of two classes of test statistics are derived under the null hypothesis and the consistency are proved under the alternative hypothesis. A bootstrap method is proposed to calculate the critical value of the empirical characteristic function statistic, and the convergence is proved. Simulation results show the effectiveness of the proposed method.(3) By constructing the efficient score statistics, we first extend the changepoints detection and monitoring to multinomial logistic regression and cumulative logistic regression models. The asymptotic distributions of our test statistics are obtained under the null hypothesis and the consistency are proved under the alternative hypothesis. Simulation results and empirical application demonstrate the validity of the proposed method.(4) A CUSUM procedure is employed to detect the variance change-points in general panel data models and the coefficient change-points in fixed effects panel data models. The asymptotic distributions of the CUSUM test statistics are derived under the null hypothesis and the consistency are proved under the alternative hypothesis. Simulation results and empirical application show the effectiveness of the proposed method.