Discussiones Mathematicae Probability and Statistics 24(1) (2004) 5-40

ON THE CONSISTENCY OF SIEVE BOOTSTRAP PREDICTION INTERVALS FOR STATIONARY TIME SERIES

Roman Różański and Adam Zagdański

Institute of Mathematics
Wrocław University of Technology
e-mail:rozanski@im.pwr.wroc.pl
e-mail:zagdan@im.pwr.wroc.pl

Abstract

In the article, we consider construction of prediction intervals for stationary time series using Bühlmann's [8], [9] sieve bootstrapapproach. Basic theoretical properties concerning consistency are proved. We extend the results obtained earlier by Stine [21], Masarotto and Grigoletto [13] for an autoregressive time series of finite order to the rich class of linear and invertible stationary models. Finite sample performance of the constructed intervals is investigated by computer simulations.

Keywords: prediction intervals, sieve bootstrap, method of sieves.

2000 Mathematics Subject Classification: 62G09, 62G15, 62M20.

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Received 14 July 2003
Revised 6 January 2004