The Study Of Periodic ARMA Model And Its Application

Time series analysis is one of important branch in probability and statistics. Recently, the theory and application of time series is developed quickly. According to the characteristic of statistics, time series is divided into two classes. One is stationary time series, the other is non-stationary time series. The non-stationary time series presents obvious tendency and periodicity. The research of the modeling of non-stationary time series is very important in practice.Firstly, some basic knowledge of time series was introduced. Then some traditional research methods of modeling the non-stationary time series are introduced in the study. The emphasis of the study is the research of modeling periodic stationary time series, it includes the five points:(ⅰ) In modeling phase, mathematical formulation of PARMA model was developed, and the characters of PARMA model were also given.(ⅱ) In the estimate phase, the innovation algorithm, developed by Meerschaer and Vecchia(1999), was used to obtain parameters estimates for PARMA models. The MATLAB program was compiled to realize the innovation algorithm.(ⅲ) The asymptotic distribution for PMA process was studied when the innovation exits finite fourth moment. The Vector Difference Equation of theψ-weights of the PARMA process was given. The order of the PMA can be identified and the parameters' estimators can be got by using the innovation algorithm, which was developed by Meerschaer and Vecchia(1999).(ⅳ) Simulated data was used to investigate the practical utility of the innovation algorithm for model identification of seasonally correlated data.(ⅴ) The application of the PARMA model and innovation algorithm was given. Flow data of tide season and dry season of Tongguan was used.