ArticleOriginal scientific text
Title
On the consistency of sieve bootstrap prediction intervals for stationary time series
Authors 1, 1
Affiliations
- Institute of Mathematics, Wrocław University of Technology
Abstract
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
Bibliography
- A.M. Alonso, D. Peña and J. Romo, Introducing model uncertainty in time series bootstrap, Working Paper, Statistics and Econometric Series, Universidad Carlos III de Madrid 9 (2001), 1-14.
- A.M. Alonso, D. Peña and J. Romo, Forecasting time series with sieve bootstrap, Journal of Statistical Planning and Inference, 100 (2002), 1-11.
- T. Anderson, The Statistical Analysis of Time Series, Wiley, New York 1971.
- Y.K. Belyaev, The continuity theorem and its application to resampling from sums of random variables, Theory of Stochastic Processes 3 (19) (1997), 100-109.
- Y.K. Belyaev and S. Sjöstedt - de Luna, Weakly approaching sequences of random distributions, Journal of Applied Probability 37 (2000), 807-822.
- P. Brockwell and R. Davis, Time Series Theory and Method, Springer-Verlag 1987.
- P. Bühlmann, Moving-average representation of autoregressive approximations, Stochastic Processes and their Applications 60 (1995), 331-342.
- P. Bühlmann, Sieve bootstrap for time series, Bernouli 3 (2) (1997), 123-148.
- P. Bühlmann, Sieve bootstrap for smoothing in nonstationary time series, The Annals of Statistics 26 (1) (1998), 48-83.
- P. Bühlmann, Bootstraps for Time Series, Statistical Science 17 (1) (2002), 52-72.
- R. Cao, et al, Saving Computer time in constructing consistent bootstrap prediction intervals for autoregressive processes, Comm. Statist. Simulation Comput. 26 (3) (1997), 961-978.
- M. Deistler and E.J. Hannan, The Statistical Theory of Linear Systems, Wiley, New York 1988.
- M. Grigoletto, Bootstrap prediction intervals for autoregressions: some alternatives, International Journal of Forecasting 14 (1998), 447-456.
- U. Grenander, Abstract Inference, Wiley, New York 1981.
- E.J. Hannan and L. Kavalieris, Regressions, autoregression models, Journal Time Series Analysis 7 (1986), 27-49.
- J.H. Kim, Bootstrap-after-bootstrap prediction intervals for autoregressive models, Journal of Business & Economic Statistics 19 (1) (2001), 117-128.
- G. Masarotto, Bootstrap prediction intervals for autoregressions, International Journal of Forecasting 6 (1990), 229-239.
- A.M. Polansky, Stabilizing bootstrap-t confidence intervals for small samples, The Canadian Journal of Statistics 28 (3) (2000), 501-516.
- D.N. Politis, J.P. Romano and M. Wolf, Subsampling, Springer-Verlag, New York 1999.
- J. Shao and D. Tu, The Jacknife and Bootstrap, Springer-Verlag, New York 1995.
- R.A. Stine, Estimating properties of autoregressive forecast, Journal of the American Statistical Association 82 (400) (1987), 1073-1078.
- L.A. Thombs and R. Schucany, Bootstrap prediction intervals for autoregression, Journal of the American Statistical Association 85 (410) (1990), 486-492.
Pages:
5-40
Main language of publication
English
Received
2003-07-14
Accepted
2004-01-06
Published
2004
DOI: 10.7151/dmps.1044
Exact and natural sciences