Chen, GemaiGuan, Zixiang2019-01-032019-01-032018-12-19Guan, Z. (2018). Nonparametric Change Point Detection for Univariate and Multivariate Non-Stationary Time Series (Doctoral thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca.http://hdl.handle.net/1880/109390This thesis investigates the change point detection problem for non-stationary time series in a nonparametric way. Two topics, which are nonparametric change point detection method for univariate time series and multivariate time series, are studied respectively. In the first topic, we consider a nonparametric method for detecting change points in non-stationary time series. The proposed method will divide the time series into several segments so that between two adjacent segments, the normalized spectral density functions are different. The theory is based on the assumption that within each segment, time series is linear process, which means that our method works not only for causal and invertible ARMA process, but also can be applied to non-invertible Moving Average process. We show that our estimations for change points are consistent. Also, a Bayesian information criterion is applied to estimate the member of change points consistently. Simulation results as well as empirical results will be presented. A nonparametric method for detecting change points in multivariate non-stationary time series is our second topic. Under the assumption that non-stationary time series consists of several stationary ones, samples will be segmented into several stationary parts so that between two adjacent time series, the normalized eigenvalues of spectral density matrices are different. Also, we assume that stationary time series are multivariate linear processes, which means that our method works for several classic multivariate time series model, e.g., ARMA process, non-invertible moving average process, which is not considered much in literature. We show that our estimations for change points are consistent. Also, a Bayesian information criterion is applied to estimate the number of change points consistently, which is similar to the univariate case.enUniversity of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.Time SeriesChange Point DetectionBIC CriterionSpectrumStatisticsdoctoral thesishttp://dx.doi.org/10.11575/PRISM/35665