Geodesic
On the consistency of sieve bootstrap prediction intervals for stationary time series
Discussiones Mathematicae. Probability and Statistics, Tome 24 (2004) no. 1, pp. 5-40

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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 
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Różański, Roman; Zagdański, Adam. On the consistency of sieve bootstrap prediction intervals for stationary time series. Discussiones Mathematicae. Probability and Statistics, Tome 24 (2004) no. 1, pp. 5-40. http://geodesic.mathdoc.fr/item/DMPS_2004_24_1_a0/