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Bootstrap Joint Prediction Regions
Author(s) -
Wolf Michael,
Wunderli Dan
Publication year - 2015
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/jtsa.12099
Subject(s) - sequence (biology) , mathematics , path (computing) , monte carlo method , joint (building) , term (time) , random variable , set (abstract data type) , variable (mathematics) , joint probability distribution , construct (python library) , statistics , econometrics , computer science , architectural engineering , mathematical analysis , genetics , physics , quantum mechanics , engineering , biology , programming language
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.