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

摘要

In the paper, the construction of unconditional bootstrap prediction intervalsand regions for some class of second order stationary multivariate linear time seriesmodels is considered. Our approach uses the sieve bootstrap procedure introducedby Kreiss (1992) and Bühlmann (1997). Basic theoretical results concerning consistencyof the bootstrap replications and the bootstrap prediction regions are proved. Wepresent a simulation study comparing the proposed bootstrap methods with the Box–Jenkins approach.