Wavelet-based estimation for seasonal long-memory processes

Technometrics

Volumn 46, Issue 2, 2004, Pages 225-238

  Whitcher, Brandon ^a  

^a NATIONAL CENTER FOR ATMOSPHERIC RESEARCH   (United States)

Author keywords

Discrete wavelet packet transform; Gegenbauer process; Maximum likelihood estimation; Ordinary least squares; Time series; Wavelet variance

Indexed keywords

DATA STORAGE EQUIPMENT; FOURIER TRANSFORMS; MATHEMATICAL MODELS; MAXIMUM LIKELIHOOD ESTIMATION; NATURAL FREQUENCIES; PARAMETER ESTIMATION; PROBABILITY DENSITY FUNCTION; SPECTRUM ANALYSIS; SPECTRUM ANALYZERS; TIME SERIES ANALYSIS;

DISCRETE WAVELET PACKET TRANSFORM (DWPT); GEGENBAUER PROCESS; ORDINARY LEAST SQUARES; WAVELET VARIANCE;

WAVELET TRANSFORMS;

EID: 2442451564     PISSN: 00401706     EISSN: None     Source Type: Trade Journal    
DOI: 10.1198/004017004000000275     Document Type: Article

References (36)

1. Anděl, J. (1986), "Long Memory Time Series Models," Kybernetika 22, 105-123.
2. Arteche, J., and Robinson, P. M. (1999), "Seasonal and Cyclical Long Memory," in Asymptotics, Nonparametrics, and Time Series, ed. S. Ghosh, New York: Marcel Dekker, pp. 115-148.
3. _ (2000), "Semiparametric Inference in Seasonal and Cyclical Long Memory Processes," Journal of Time Series Analysis, 21, 1-25.
4. Beran, J. (1994), Statistics for Long-Memory Processes, New York: Chapman & Hall.
5. Brockwell, P. J., and Davis, R. A. (1991), Time Series: Theory and Methods (2nd ed.), New York: Springer-Verlag.
6. Brown, R. L., Durbin, J., and Evans, J. M. (1975), "Techniques for Testing the Constancy of Regression Relationships Over Time," Journal of the Royal Statistical Society, Ser. B, 37, 149-163.
7. Chung, C.-F. (1996a), "Estimating a Generalized Long Memory Process," Journal of Econometrics, 73, 237-259.
8. _ (1996b), "A Generalized Fractionally Integrated Autoregressive Moving Average Process," Journal of Time Series Analysis 17, 111-14.
9. Daubechies, I. (1992), Ten Lectures on Wavelets, Philadelphia: Society for Industrial and Applied Mathematics.
10. Fouskitakis, G. N., and Fassois, S. D. (1999), "Pseudolinear Estimation of Fractionally Integrated ARMA (ARFIMA) Models With Automotive Application," IEEE Transactions on Signal Processing, 47, 3365-3380.
11. Gençay, R., Selçuk, F., and Whitcher, B. (2001), An Introduction to Wavelets and Other Filtering Methods in Finance and Economics, San Diego: Academic Press.
12. Geweke, J., and Porter-Hudak, S. (1983), "The Estimation and Application of Long Memory Time Series Models," Journal of Time Series Analysis, 4, 221-238.
13. Gray, H. L., Zhang, N.-F., and Woodward, W. A. (1989), "On Generalized Fractional Processes," Journal of Time Series Analysis, 10, 233-257.
14. Greenhall, C. A. (1991), "Recipes for Degrees of Freedom of Frequency Stability Estimators," IEEE Transactions on Instrumentation and Measurement, 40, 994-999.
15. Hosking, J. R. M. (1981), "Fractional Differencing," Biometrika, 68, 165-176.
16. _ (1984), "Modeling Persistence in Hydrological Time Series Using Fractional Differencing," Water Resources Research, 20, 1898-1908.
17. Jensen, M. J. (1999a), "An Approximate Wavelet MLE of Short and Long Memory Parameters," Studies in Nonlinear Dynamics and Economics, 3, 239-253.
18. _ (1999b), "Using Wavelets to Obtain a Consistent Ordinary Least Squares Estimator of the Long-Memory Parameter," Journal of Forecasting, 18, 17-32.
19. Lapsa, P. M. (1997), "Determination of Gegenbauer-Type Random Process Models," Signal Processing, 63, 73-90.
20. Lobato, I. N. (1997), "Semiparametric Estimation of Seasonal Long-Memory Models: Theory and Application to Modeling of Exchange Rates," Investigaciones Económicas, 21, 273-295.
21. McCoy, E. J., and Walden, A. T. (1996), "Wavelet Analysis and Synthesis of Stationary Long-Memory Processes," Journal of Computational and Graphical Statistics, 5, 26-56.
22. Morris, J. M., and Peravali, R., (1999), "Minimum-Bandwidth Discrete-Time Wavelets," Signal Processing, 76, 181-193.
23. Ooms, M. (1995), "Flexible Seasonal Long Memory and Economic Time Series," Technical Report 9515/A, Econometric Institute, Erasmus University.
24. Percival, D. B. (1995), "On estimation of the Wavelet Variance," Biometrika, 82, 619-631.
25. Percival, D. B., and Walden, A. T. (1993), Spectral Analysis for Physical Applications: Multitaper and Conventional Univariate Techniques, Cambridge, U.K.: Cambridge University Press.
26. _ (2000), Wavelet Methods for Time Series Analysis, Cambridge, U.K.: Cambridge University Press.
27. Piessons, R., de Doncker-Kapenga, E., Überhuber, C. W., and Kahaner, D. K. (1983), QUADPACK: A Subroutine Package for Automatic Integration, Heidelberg: Springer-Verlag.
28. Ramachandran, R., and Beaumont, P. (2001), "Robust Estimation of GARMA Model Parameters With an Application to Cointegration Among Interest Rates of Industrialized Countries," Computational Economics, 17, 179-201.
29. Ray, B. K. (1993), "Long-Range Forecasting of IBM Product Revenues Using a Seasonal Fractionally Differenced ARMA Model," International Journal of Forecasting, 9, 255-269.
30. Riedel, K. S., and Sidorenko, A. (1995), "Minimum Bias Multiple Taper Spectral Estimation," IEEE Transactions on Signal Processing, 43, 188-195.
31. Robinson, P. M. (1995), "Log-Periodogram Regression of Time Series With Long-Range Dependence," The Annals of Statistics, 23, 1048-1072.
32. Thomson, D. J. (1982), "Spectrum Estimation and Harmonic Analysis," IEEE Proceedings, 70, 1055-1096.
33. Whitcher, B. (2001), "Simulating Gaussian Stationary Processes With Unbounded Spectra," Journal of Computational and Graphical Statistics, 10, 112-134.
34. Whitcher, B., Byers, S. D., Guttorp, P., and Percival, D. B. (2002), "Testing for Homogeneity of Variance in Time Series: Long Memory, Wavelets and the Nile River," Water Resources Research, 38, doi: 10.1029/2001WR000509.
35. Wickerhauser, M. V. (1994), Adapted Wavelet Analysis: From Theory to Software, Wellesley, MA: A. K. Peters.
36. Woodward, W. A., Cheng, Q. C., and Gray, H. L. (1998), "A k-Factor GARMA Long-Memory Model," Journal of Time Series Analysis, 19, 485-504.