Approximate predictive pivots for autoregressive processes

In this paper the author considers an autoregressive process where the parameters of the process are unknown and try to obtain pivots for predicting future observations. If we do a probabilistic prediction with the estimated model, where the parameters are estimated by a sample of size n, we introduce an error of order n−1 in the coverage probabilities of the prediction intervals. However we can reduce the order of the error if we calibrate adequately the estimated prediction bounds. The solution obtained can be expressed in terms of an approximate predictive pivot.