On Bootstrap Predictive Inference For Autoregressive Processes

. In this paper we consider bootstrap‐based predictive inference for autoregressive processes of order p. We consider both unconditional inference and inference conditional on the last p observed values. We make two contributions. Our first contribution is to point out the best way to apply the bootstrap to unconditional predictive inference when the process is Gaussian. Now, it may be argued that predictive inference for autoregressive processes of order p should be carried out conditional on the last p observed values. When the process is Gaussian, a bootstrap predictive inference conditional on the last p observed values is conveniently computed by ‘running’ the same autoregressive process backwards in time. This procedure is inappropriate for non‐Gaussian autoregressive processes. Our second (and more important) contribution is to present a method (which is not computationally burdensome) for the computation of a bootstrap predictive inference for a non‐Gaussian autoregressive process of order p conditional on the last p observed values.