ABSTRACT
The aim of this chapter is to illustrate the application of a class of linear time series models, called ZAR models, which have been introduced to the literature in recent years. They are a generalization of linear autoregressive (AR) models that have the potential to improve the long range prediction of time series by extending the dependence on past values to high lags. We will review earlier work on these models at the end of this section. We describe them in Section 21.3, and present their properties and estimation procedures in the following sections. A ZAR model is specified by its order, p, and a smoothing coefficient, θ, and reduces to an AR(p) model when θ = 0. Standard AR (and ARIMA) models are widely and successfully used, but there are examples that suggest that we should be able to improve upon the predictions that they furnish. The specific example we use to illustrate the topics in this chapter is the series of the monthly USA unemployment rate from January 1968 to August 2009. In this section, we consider long range forecasting issues typified by this example series, and in the next section we present forecasts of the series which illustrate the ability of the ZAR model to address these issues.
