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.