A histogram sieve estimator of the drift function in Ito processes and some semimartingales is constructed. It is proved that the estimator is pointwise and L¹ consistent and its finite-dimensional distributions are asymptotically normal. Our approach extends the results of Leśkow and Różański (1989a).
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.
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