Properties of the sieve bootstrap for fractionally integrated and non-invertible processes

Journal of Time Series Analysis

Volumn 29, Issue 2, 2008, Pages 224-250

  Poskitt, D S ^a  

^a MONASH UNIVERSITY   (Australia)

Author keywords

Autoregressive approximation; Fractional process; Non invertibility; Rate of convergence; Sieve bootstrap

Indexed keywords

EID: 39749105243     PISSN: 01439782     EISSN: 14679892     Source Type: Journal    
DOI: 10.1111/j.1467-9892.2007.00554.x     Document Type: Article

References (39)

1. Akaike, H. (1969) Fitting autoregressive models for prediction. Annals of Institute of Statistical Mathematics 21, 243 7.
2. Andrews, D. Lieberman, O. (2005) Valid Edgeworth expansions for the Whittle maximum likelihood estimator for stationary long-memory gaussian time series. Econometric Theory 21, 710 34.
3. Andrews, D., Lieberman, O. Marmer, V. (2006) Higher-order improvements of the parametric bootstrap for long-memory gaussian processes. Journal of Econometrics 133, 673 702.
4. Andrews, D. W. K. (2004) The block-block bootstrap: improved asymptotic refinements. Econometrica 72, 673 700.
5. Apostol, T. M. (1960) Mathematical Analysis. Reading : Addison-Wesley.
6. Baillie, R. T. (1996) Long memory processes and fractional integration in econometrics. Journal of Econometrics 73, 5 59.
7. Baxter, G. (1962) An asymptotic result for the finite predictor. Math. Scand. 10, 137 44.
8. Beran, J. (1992) Long-range dependence. Statistical Science 7, 404 27.
9. Beran, J. (1994) Statistics for Long Memory Processes. New York : Chapman and Hall.
10. Berk, K. N. (1974) Consistent autoregressive spectral estimation. Annals of Statistics 2, 489 502.
11. Bickel, P. J. Freedman, D. A. (1981) Some asymptotic theory for the bootstrap. Annals of Statistics 9, 1196 217.
12. Bühlmann, P. (1997) Sieve bootstrap for time series. Bernoulli 3, 123 48.
13. Burg, J. (1968) A new analysis technique for time series data. Tech. Rep., N.A.T.O., Enschede, the Netherlands : Advanced Study Institute on Signal Processing.
14. Choi, E. Hall, P. G. (2000) Bootstrap confidence regions from autoregressions of arbitrary order. Journal of the Royal Statistical Society B 62, 461 77.
15. Durbin, J. (1960) The fitting of time series models. Review of International Statistical Institute 28, 233 44.
16. Durbin, J. (1980) Approximations for densities of sufficient estimators. Biometrika 67, 311 33.
17. Granger, C. W. J. Joyeux, R. (1980) An introduction to long-memory time series models and fractional differencing. Journal of Time Series Analysis 1, 15 29.
18. Grose, S. Poskitt, D. S. (2006) The finite-sample properties of autoregressive approximations of fractionally-integrated and non-invertible processes. Tech. Rep., Department of Econometrics & Business Statistics, Working Paper 15/06, Monash University. http://www.buseco.monash.edu.au/depts/ ebs/pubs/wpapers.
19. Hannan, E. J. Deistler, M. (1988) The Statistical Theory of Linear Systems. New York : Wiley.
20. Horowitz, J. L. (2003) Bootstrap methods for markov processes. Econometrica 71, 1049 82.
21. Hosking, J. R. M. (1980) Fractional differencing. Biometrika 68, 165 76.
22. Hosking, J. R. M. (1996) Asymptotic distributions of the sample mean, autocovariances, and autocorrelations of long memory time series. Journal of Econometrics 73, 261 84.
23. Kolmorgorov, A. N. (1941) Interpolation und extrapolation von stationaren zufalligen folgen. Bulletin Academy Science U. S. S. R., Mathematics Series 5, 3 14.
24. Künsch, H. R. (1989) The jacknife and the bootstrap for general stationary observations. Annals of Statistics 17, 1217 41.
25. Levinson, N. (1947) The Wiener RMS (root mean square) error criterion in filter design and prediction. Journal of Mathematical Physics 25, 261 78.
26. Lieberman, O. Phillips, P. C. B. (2004) Expansions for the distribution of the maximum likelihood estimator of the fractional difference parameter. Econometric Theory 20, 464 484.
27. Lieberman, O., Rousseau, J. Zucker, D. M. (2003) Valid asymptotic expansions for the maximum likelihood estimator of the parameter of a stationary Gaussian strongly dependent process. Annals of Statistics 31, 586 612.
28. p. Technometrics 15, 661 75.
29. Munroe, M. E. (1953) Introduction to Measure and Integration. Reading : Addison-Wesley.
30. Parzen, E. (1974) Some recent advances in time series modelling. IEEE Transactions on Automatic Control AC-19, 723 30.
31. Paulsen, J. Tjøstheim, D. (1985) On the estimation of residual variance and order in autoregressive time series. Journal of the Royal Statistical Society B-47, 216 28.
32. Poskitt, D. S. (2006) Autoregressive approximation in nonstandard situations: the fractionally integrated and non-invertible cases. Annals Institute Statistical Mathematics Forthcoming. See http://www.ism.ac.jp/editsec/ alsm/forthcoming_all.html
33. Shibata, R. (1980) Asymptotically efficient selection of the order of the model for estimating parameters of a linear process. Annals of Statistics 8, 147 64.
34. Szegö, G. (1939) Orthogonal Polynomials. Providence : American Mathematical Society Colloquium Publication.
35. Taniguchi, M. (1984) Validity of Edgeworth expansions for statistics of time series. Journal of Time Series Analysis 5, 37 51.
36. Tjøstheim, D. Paulsen, J. (1983) Bias of some commonly-used time series estimators. Biometrika 70, 389 400.
37. Wand, M. Jones, M. C. (1995) Kernel Smoothing. London : Chapman and Hall.
38. Wold, H. (1938) The Analysis of Stationary Time Series (2nd edn). Uppsala : Almquist and Wicksell.
39. Zhang, Y. McLeod, A. I. (2005) Computer algebra derivation of the bias of linear estimators of autoregressive models. Journal of Time Series Analysis 27, 157 65.