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Prediction intervals and regions for multivariate time series models with sieve bootstrap

Różański R., Chłapiński G., Hławka M., Jamróz K., Kawecki M., Zagdański A.

Probability and Mathematical Statistics

2018

Vol. 38, Fasc. 2

317--357

In the paper, the construction of unconditional bootstrap prediction intervals and regions for some class of second order stationary multivariate linear time series models is considered. Our approach uses the sieje bootstrap procedure introduced by Kreiss (1992) and Bühlmann (1997). Basic theoretical results concerning consistency of the bootstrap replications and the bootstrap prediction regions are proved. We present a simulation study comparing the proposed bootstrap methods with the Box-Jenkins approach.