A two-step approach for identifying seasonal autoregressive time series forecasting models

One of the most powerful and widely used methodologies for forecasting economic time series is the class of models known as seasonal autoregressive processes. In this article we present a new approach not only for identifying seasonal autoregressive models, but also the degree of differencing required to induce stationarity in the data. The identification method is iterative and consists in systematically fitting increasing order models to the data, and then verifying that the resulting residuals behave like white noise using a two stage autoregressive order determination criterion. Once the order of the process is determined the identified structure is tested to see if it can be simplified. The identification performance of this procedure is contrasted with other order selection procedures for models with ‘gaps’. We also illustrate the forecast performance of the identification method using monthly and quarterly economic data.