Recent developments in bootstrap methods for dependent data

Giuseppe Cavaliere, Dimitris N. Politis, Anders Rahbek, Michael Wolf and Dan Wunderli

Journal of Time Series Analysis, 2015, vol. 36, issue 3, 352-376

Abstract: type="main" xml:id="jtsa12099-abs-0001"> 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.

Date: 2015
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