Modeling Power Exponential Error Innovations with Autoregressive Process

The regular gussian assumption of the error terms is employed in dynamic time series models when the underlying data are not normally distributed, this often results in incorrect parameter estimations and forecast error. As a result, this paper developed maximum likelihood method of estimation of parameters of an autoregressive model of order 2 [AR (2)] with power-exponential innovations. The performance of the parameters of AR (2) in comparison to normal error innovations was evaluated using the Akaike information criterion (AIC) and forecast performance metrics (RMSE and MAE). Both real data sets and simulated data with different sample sizes were used to validate the models. The results revealed that, it is more appropriate and efficient to model non-normal time series data using AR (2) exponential power error innovations.