Chapter X - FORMULATION AND ESTIMATION OF MIXED MOVING-AVERAGE AUTOREGRESSIVE MODELS FOR SINGLE TIME SERIES: EXAMPLES

Abstract

In most analyses of economic time series, it is necessary to remove a polynomial trend or difference the series to render them stationary. Series that follows a mixed autoregressive moving-average (ARMA) model is said to follow an autoregressive integrated moving-average (ARIMA) model. This chapter presents the formulation and estimation of mixed ARMA models for single time series. It describes seasonal models. The proposed procedure for seasonal models can also be used for nonseasonal models. The proposed method is a variation of Box and Jenkins' procedure (1970). Having formulated a time-series model for a series, the parameters of the model can be estimated in the time domain or in the frequency domain. The frequency domain estimates for the parameters are much simpler to obtain. The chapter presents the comparison between estimation methods in the frequency and time domains. The comparison of the two estimation procedures is made by means of comparing the forecast ability of the models under the two sets of parameters obtained by the different estimation.