Linear Autoregression for Prediction: Small Sample Inference

This paper describes inferences based on linear predictors for stationary time series. These methods are flexible, since relatively few assumptions are needed to fit a linear predictor. A confidence interval for the resulting predicted value, which takes account of the variance of the estimated parameters, is discussed. The possible non-parsimony of the linear prediction compared to the classical ARMA forecasting method is a drawback often mentioned in the literature. On the other hand, as we show in a small simulation study, the usual predictive inference based on an ARMA modelling is overoptimistic in small samples, whereas the coverage rate of our confidence interval is close to the nominal value even for small series.