ON THE CONSTRUCTION AND PROPERTIES OF BOOTSTRAP-
PREDICTION INTERVALS FOR STATIONARY TIME SERIES
Abstract: We consider the construction of unconditional bootstrap-t prediction intervals for
stationary time series. Our approach relies on the sieve bootstrap resampling scheme
introduced by Bühlmann [8].
Basic theoretical properties concerned with consistency of the bootstrap approximation as
well as consistency of constructed intervals are proved.
We generalize results obtained earlier by Stine [26], Masarotto [21] and Grigoletto [16]
for autoregressive time series of finite order to the rich class of linear and invertible stationary
models.
Finite sample accuracy of proposed bootstrap-t prediction intervals is verified
by computer simulations. Empirical results of a comparative study show that our
method is a superior alternative to both traditional Box-Jenkins approach and hybrid
sieve-bootstrap prediction intervals proposed recently by Różański and Zagdański [24].
2000 AMS Mathematics Subject Classification: 62G09, 62G15, 62M20.
Key words and phrases: Prediction intervals, sieve bootstrap-t method of sieves.