Analysis of Nonstationary Time Series With Time Varying Frequencies Piecewise M-Stationary Process

This thesis focuses on the analysis of nonstationary processes with linearly time vary-ing periodic behavior. First we develop LM-stationary processes for analyzing time series data with linearly compacting periodic behavior. Spectral analysis using this method shows better performance than that using the Wigner-Ville time frequency distribution. The LM-stationary forecasts produce better results than autoregressive forecasts applied directly to time series data with linearly compacting periods. The second part of this thesis develops piecewise G-stationary processes and develops the piecewise M-stationary process which is capable of analyzing data with linear periodic change that is piecewise monotonic. The in-stantaneous spectrum obtained using this model is able to capture the change of frequency behavior more clearly than the standard Wigner-Ville time frequency distribution. The time varying frequency obtained using the Wigner-Ville time frequency distribution is used in the detection of the change point. LM-stationary and RM-stationary models are used in appropriate time intervals where frequencies are changing monotonically. In addition to two main developments, this thesis discusses properties of G-stationary, piecewise G-stationary and extended G-stationary processes.