Projected polynomial autoregression for prediction of stationary time series

Abstract

Polynomial autoregressions are usually considered to be unrealistic models for time series. However, this paper shows that they can successfully be used when the purpose of the time series study is to provide forecasts. A projection scheme inspired from projection pursuit regression and feedforward artificial neural networks is used in order to avoid an explosion of the number of parameters when considering a large number of lags. The estimation of the parameters of the projected polynomial autoregressions is a non-linear least-squares problem. A consistency result is proved. A simulation study shows that the naive use of the common final prediction error criterion is inappropriate to identify the best projected polynomial autoregression. An explanation of this phenomenon is given and a correction to the criterion is proposed. An important feature of the polynomial predictors introduced in this paper is their simple implementation, which allows for automatic use. This is illustrated with real data for the three-month US Treasury Bill.