Bootstrap Joint Prediction Regions. (14th October 2014)

• Record Type: Journal Article
• Authors: Wolf, Michael; Wunderli, Dan
• Other Names: Cavaliere Giuseppe guestEditor.; Politis Dimitris N. guestEditor.; Rahbek Anders guestEditor.
• Is Part Of: Journal of time series analysis. Volume 36:Number 3(2015:May)
• Page Start: 352
• Page End: 376
• Publication Date: 2014-10-14
• Subjects: Generalized error rates -- path forecast -- simultaneous prediction intervals; Time-series analysis -- Periodicals; 519.232
• DOI: 10.1111/jtsa.12099
• Languages: English
• ISSNs: 0143-9782

Abstract

Abstract : 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.