Identification Of Periodic Autoregressive Moving-Average Time Series Models With R

Abstract

Periodic autoregressive moving average PARMA process extend the classical autoregressive moving average ARMA process by allowing the parameters to vary with seasons. Model identification is the identification of a possible model based on an available realization, i.e., determining the type of the model with appropriate orders. The Periodic Autocorrelation Function (PeACF) and the Periodic Partial Autocorrelation Function (PePACF) serve as useful indicators of the correlation or of the dependence between the values of the series so that they play an important role in model identification. The identification is based on the cut-off property of the Periodic Autocorrelation Function (PeACF). We derive an explicit expression for the asymptotic variance of the sample PeACF to be used in establishing its bands. Therefore, we will get in this study a new structure of the periodic autocorrelation function which depends directly to the variance that will derived to be used in establishing its bands for the PMA process over the cut-off region and we have studied the theoretical side and we will apply some simulated examples with R which agrees well with the theoretical results.