Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-27T18:43:51.536Z Has data issue: false hasContentIssue false
  • English
  • Français

VALIDITY OF THE SAMPLING WINDOW METHOD FOR LONG-RANGE DEPENDENT LINEAR PROCESSES

Published online by Cambridge University Press:  23 September 2005

Daniel J. Nordman  and
Soumendra N. Lahiri
Daniel J. Nordman
Affiliation:
Iowa State University
Soumendra N. Lahiri
Affiliation:
Iowa State University
Get access Rights & Permissions [Opens in a new window]

Abstract

The sampling window method of Hall, Jing, and Lahiri (1998, Statistica Sinica 8, 1189–1204) is known to consistently estimate the distribution of the sample mean for a class of long-range dependent processes, generated by transformations of Gaussian time series. This paper shows that the same nonparametric subsampling method is also valid for an entirely different category of long-range dependent series that are linear with possibly non-Gaussian innovations. For these strongly dependent time processes, subsampling confidence intervals allow inference on the process mean without knowledge of the underlying innovation distribution or the long-memory parameter. The finite-sample coverage accuracy of the subsampling method is examined through a numerical study.The authors thank two referees for comments and suggestions that greatly improved an earlier draft of the paper. This research was partially supported by U.S. National Science Foundation grants DMS 00-72571 and DMS 03-06574 and by the Deutsche Forschungsgemeinschaft (SFB 475).

Type
Research Article
Information
Econometric Theory , Volume 21 , Issue 6 , December 2005 , pp. 1087 - 1111
Copyright
© 2005 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Adenstedt, R.K. (1974) On large-sample estimation for the mean of a stationary sequence. Annals of Statistics 2, 1095–1107.Google Scholar
Bardet, J., G. Lang, G. Oppenheim, S. Philippe, & M.S. Taqqu (2003) Generators of long-range dependent processes: A survey. In P. Doukhan, G. Oppenheim, & M.S. Taqqu (eds.), Theory and Applications of Long-Range Dependence, pp. 579–624. Birkhäuser.
Bardet, J., G. Lang, G. Oppenheim, A. Philippe, S. Stoev, & M.S. Taqqu (2003) Semi-parametric estimation of the long-range dependence parameter: A survey. In P. Doukhan, G. Oppenheim, & M.S. Taqqu (eds.), Theory and Applications of Long-Range Dependence, pp. 527–556. Birkhäuser.
Beran, J. (1989) A test of location for data with slowly decaying serial correlations. Biometrika 76, 261–269.Google Scholar
Beran, J. (1994) Statistical Methods for Long Memory Processes. Chapman & Hall.
Bingham, N.H., C.M. Goldie, & J.L. Teugels (1987) Regular Variation. Cambridge University Press.
Carlstein, E. (1986) The use of subseries methods for estimating the variance of a general statistic from a stationary time series. Annals of Statistics 14, 1171–1179.Google Scholar
Davydov, Y.A. (1970) The invariance principle for stationary processes. Theory of Probability and Its Applications 15, 487–498.Google Scholar
Dobrushin, R.L. & P. Major (1979) Non-central limit theorems for non-linear functionals of Gaussian fields. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 50, 827–842.Google Scholar
Doukhan, P. (1994) Mixing: properties and examples. Lecture Notes in Statistics 85, Springer-Verlag.
Fuller, W. (1996) Introduction to Statistical Time Series, 2nd ed. Wiley.
Granger, C.W.J. & R. Joyeux (1980) An introduction to long-memory time series models and fractional differencing. Journal of Time Series Analysis 1, 15–29.Google Scholar
Geweke, J. & S. Porter-Hudak (1983) The estimation and application of long-memory time series models. Journal of Time Series Analysis 4, 221–238.Google Scholar
Hall, P., J.L. Horowitz, & B.-Y. Jing (1995) On blocking rules for the bootstrap with dependent data. Biometrika 82, 561–574.Google Scholar
Hall, P. & B.-Y. Jing (1996) On sample reuse methods for dependent data. Journal of the Royal Statistical Society, Series B 58, 727–737.Google Scholar
Hall, P., B.-Y. Jing, & S.N. Lahiri (1998) On the sampling window method for long-range dependent data. Statistica Sinica 8, 1189–1204.Google Scholar
Henry, M. & P. Zaffaroni (2003) The long-range dependence paradigm for macroeconomics and finance. In P. Doukhan, G. Oppenheim, & M.S. Taqqu (eds.), Theory and Applications of Long-Range Dependence, pp. 417–438. Birkhäuser.
Hosking, J.R.M. (1981) Fractional differencing. Biometrika 68, 165–176.Google Scholar
Hurvich, C.M., R. Deo, & J. Brodsky (1998) The mean square error of Geweke and Porter-Hudak's estimator of the memory parameter of a long memory time series. Journal of Time Series Analysis 19, 19–46.Google Scholar
Ibragimov, I.A. & Y.V. Linnik (1971) Independent and Stationary Sequences of Random Variables. Wolters-Noordhoff.
Künsch, H.R. (1989) The jackknife and bootstrap for general stationary observations. Annals of Statistics 17, 1217–1261.Google Scholar
Lahiri, S.N. (1993) On the moving block bootstrap under long range dependence. Statistics and Probability Letters 18, 405–413.Google Scholar
Liu, R.Y. & K. Singh (1992) Moving blocks jackknife and bootstrap capture weak dependence. In R. LePage and L. Billard (eds.), Exploring the Limits of Bootstrap, pp. 225–248. Wiley.
Mandelbrot, B.B. & J.W. van Ness (1968) Fractional Brownian motions, fractional noises and applications. SIAM Review 10, 422–437.Google Scholar
Montanari, A. (2003) Long-range dependence in hydrology. In P. Doukhan, G. Oppenheim, & M.S. Taqqu (eds.), Theory and Applications of Long-Range Dependence, pp. 461–472. Birkhäuser.
Politis, D.N. & J.P. Romano (1994) Large sample confidence regions based on subsamples under minimal assumptions. Annals of Statistics 22, 2031–2050.Google Scholar
Taqqu, M.S. (1975) Weak convergence to fractional Brownian motion and to the Rosenblatt process. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 31, 287–302.Google Scholar
Taqqu, M.S. (1977) Law of the iterated logarithm for sums of non-linear functions of Gaussian variables that exhibit a long range dependence. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 40, 203–238.Google Scholar
Taqqu, M.S. (1979) Convergence of integrated processes of arbitrary Hermite rank. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 50, 53–83.Google Scholar
Wood, A.T.A. & G. Chan (1994) Simulation of stationary Gaussian processes in [0,1]d. Journal of Computational and Graphical Statistics 3, 409–432.Google Scholar