Generalized Exponential Predictors for Time Series Forecasting

We consider the problem of prediction for stationary and nonstationary univariate time series using a modification suggested by the usual exponentially weighted moving average method. The modification leads to a class of general exponential predictors that can improve on the usual finite approximations to an infinite autoregressive process. We provide the theoretical justifications and suggest a class of predictors that covers modified and finite autoregressive fits as special cases. Two examples involving sample data show how the method is competitive with autoregressive integrated moving average (ARIMA) when applied to a U.S. energy use series and improves on ARIMA when applied to a global temperature series. A simulation indicates that considerable improvements are possible for infinite autoregressive (ARIMA) processes exhibiting certain special patterns of long-range dependence.