Improved frequentist prediction intervals for autoregressive models by simulation

Abstract

It is well known that the so-called plug-in prediction intervals for autoregressive processes, with Gaussian disturbances, are too short, i.e. the coverage probabilities fall below the nominal ones. However, simulation experiments show that the formulas borrowed from the ordinary linear regression theory yield one-step prediction intervals, which have coverage probabilities very close to that claimed. From a Bayesian point of view the resulting intervals are posterior predictive intervals when uniform priors are assumed for both autoregressive coefficients and logarithm of the disturbance variance. This finding enables one to see how to treat multi-step prediction intervals that are obtained by simulation either directly from the posterior distribution or using importance sampling. An application of the method to forecasting the annual gross domestic product growth in the United Kingdom and Spain is given for the period 2002 to 2011 using the estimation period 1962 to 2001.