Bootstrap joint prediction regions - Michael Wolf; Dan Wunderli (University of Zurich, Department of Economics, 2013)
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 finitesample performance of our joint prediction regions to some previous proposals via Monte Carlo simulations. An empirical application to a real data set is also provided.
Keywords: C14; C32; C53; 330; generalized error rates; path forecast; simultaneous prediction intervals; Prognoseverfahren; Bootstrap-Verfahren; Statistischer Fehler; Zeitreihenanalyse; Theorie