Bootstrap Joint Prediction Regions

Many statistical applications require the forecast of a random variable of interest over several periods into the future. The sequence of individual forecasts, one period at a time, is called a path forecast, where the term  path refers to the sequence of individual future realizations of the random variable. The problem of constructing a corresponding joint prediction region has been rather neglected in the literature so far: such a region is supposed to contain the entire future path with a prespecified probability. We develop bootstrap methods to construct joint prediction regions. The resulting regions are proven to be asymptotically consistent under a mild high‐level assumption. We compare the finite‐sample performance of our joint prediction regions with some previous proposals via Monte Carlo simulations. An empirical application to a real data set is also provided.