Bootstrapping the local periodogram of locally stationary processes

Journal of Time Series Analysis

Volumn 29, Issue 2, 2008, Pages 264-299

  Sergides, Marios ^a   Paparoditis, Efstathios ^a  

^a UNIVERSITY OF CYPRUS   (Cyprus)

Author keywords

Autoregressive processes; Bootstrap; Local periodogram; Locally stationary processes; Nonparametric estimation; Spectral means

Indexed keywords

EID: 39749185919     PISSN: 01439782     EISSN: 14679892     Source Type: Journal    
DOI: 10.1111/j.1467-9892.2007.00556.x     Document Type: Article

References (30)

1. Anderson, T. W. (1971) The Statistical Analysis of Time Series. New York : John Wiley and Sons.
2. Beltrão, K. I. Bloolfield, P. (1987) Determining the bandwidth of a kernel spectrum estimate. Journal of Time Series Analysis 8, 21 38.
3. Berk, K. N. (1974) Consistent autoregressive spectral estimates. The Annals of Statistics 2, 489 502.
4. Brillinger, D. R. (1981) Time Series: Data Analysis and Theory. San Francisco : Holden-Day.
5. Brockwell, P. Davis, R. A. (1991) Time Series: Theory and Methods (2nd edn). New York : Springer.
6. Dahlhaus, R 1996) Asymptotic statistical inference for nonstationary process with evolutionary spectra. In Athens Conference on Applied Probability and Time Series Analysis, Vol II (eds P. M. Robinson M. Rosenblatt). New York : Springer Verlag, pp. 145 59.
7. Dahlhaus, R. (1997) Fitting time series models to nonstationary processes. The Annals of Statistics 25, 1 37.
8. Dahlhaus, R 2003) Curve estimation for locally stationary time series models. In Recent Advances and Trends in Nonparametric Statistics (eds M. G. Akritas D. N. Politis). Amsterdam : Elsevier Science B.V., pp. 451 66.
9. Dahlhaus, R. Janas, D. (1996) A frequency domain bootstrap for ratio statistics in time series analysis. The Annals of Statistics 24, 1934 63.
10. Dahlhaus, R. Giraitis, L. (1998) On optimal segment length for parameter estimators for locally stationary time series. Journal of Time Series Analysis 19, 629 55.
11. Dahlhaus, R Polonik, W 2003) Nonparametric maximum likelihood estimation and empirical spectral processes for locally stationary processes. Preprint. Universitat Heidelberg.
12. Dahlhaus, R Subba Rao, S 2006) Statistical inference of time varying ARCH processes. The Annals of Statistics 34, 1075 114.
13. Dowla, A, Paparoditis, E Politis, D. N (2003) Locally stationary processes and the local block bootstrap. In Recent Advances and Trends in Non Parametric Statistics (eds M. G. Akritas D. N. Politis). Amsterdam : Elsevier Science B.V., pp. 437 44.
14. Franke, J. Härdle, W. (1992) On bootstrapping kernel spectral estimates. The Annals of Statistics 20, 121 45.
15. Grenander, U Szegö, G. (1958) Toeplitz Forms and Their Applications. Berkeley : University of California Press.
16. Hurvich, C. M Zeger, S. L 1987) Frequency domain bootstrap methods for time series. Technical Report 87-115, Graduate School of Business Administration, New York University.
17. Kreiss, J.-P 1999) Residual and wild bootstrap for infinite order autoregression. Unpublished manuscript.
18. Kreiss, J.-P. Paparoditis, E. (2003) Autoregressive-aided periodogram bootstrap for time series. The Annals of Statistics 31, 1923 55.
19. Nason, G. P., von Sachs, R. Kroisandt, G. (2000) Wavelet processes and adaptive estimation of the evolutionary wavelet spectrum. Journal of Royal Statistical Society, Series B Statistical Methodology 62, 271 92.
20. Neumann, M. von Sachs, R (1997) Wavelet thresholding in anisotropic function classes and application to adaptive estimation of evolutionary spectra. The Annals of Statistics 25, 38 76.
21. Nordgaard, A. (1992) Resampling stochastic processes using a bootstrap approach. Lecture Notes in Economics and Mathematical Systems 376, 181 85.
22. Ombao, H., Raz, J., von Sachs, R. Guo, W. (2002) The SLEX model of a non-stationary random process. Nonparametric approach to time series analysis. Annals of the Institute of Statistical Mathematics 54, 171 200.
23. Paparoditis, E 2002) Frequency domain bootstrap for time series. In Empirical Process Techniques for Dependent Data (eds H. Dehling, T. Mikosch M. Sørensen). Boston : Birkhäuser, 365 81.
24. Paparoditis, E. Politis, D. N. (1999) The local bootstrap for the periodogram. Journal of Time Series Analysis 20, 193 222.
25. Paparoditis, E. Politis, D. N. (2002) Local block bootstrap. C.R. Acad. Sci. Paris, Ser. I, 335, 959 62.
26. Priestley, M. B. (1965) Evolutionary spectra and non-stationary processes. Journal of the Royal Statistical Society, Series B 62, 204 37.
27. Priestley, M. B. (1981) Spectral Analysis and Time Series. New York : Academic Press.
28. Shumway, R. Stoffer, D. (2000) Time Series and its Applications. New York : Springer.
29. Subba Rao, S 2004) On some nonstationarity, nonlinear random processes and their stationary approximations. Preprint.
30. Theiler, J., Paul, L. S. Rubin, D. M 1994) Detecting nonlinearity in data with long coherence times. In Times Series Prediction (eds A. Weigend N. Gershenfeld). Reading, MA : Addison-Wesley, pp. 429 55.