Periodically Correlated Time Series Models: Representation and Identification

Abstract

This thesis is interested with some characteristics of a class periodically correlated (PC) time series models. We study both periodically correlated time series models and multiple models and discuss the relationship between them. Give many examples. We discuss in this work many representations of PC models and use these representations in order make evidence that PC class and multiple AR models are theoretically the same. In addition, we propose a new representation, the multi-companion (MC) representation. Give an example. We discuss the relationship between the vector moving average and the periodic moving average, and give an examples to clarify the relationship between them. Also, we study the periodic autoregressive moving-average (PARMA) models and their representations. We show that any PARMA model can be expressed as a vector ARMA model. We consider the identification of orders of periodic AR (PAR) models by extending well known techniques to periodic time series, we discuss methods for specifying models and for efficiently estimating the parameters in those models. Finally, a detailed simulation study is given to illustrate the procedures.