Bootstrap Joint Prediction Regions

Many economic and financial 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 a bootstrap method to construct such a joint prediction region. The resulting region is proven to be asymptotically consistent under a mild high-level assumption. It also has better finite-sample performance than previous proposals in the literature. KEY WORDS: Generalized error rates; path forecast; simultaneous prediction intervals. Proceedings 59th ISI World Statistics Congress, 25-30 August 2013, Hong Kong (Session CPS022) p.391