Minimum contrast estimation of random processes based on information of second and third orders

Journal of Statistical Planning and Inference

Volumn 137, Issue 4, 2007, Pages 1302-1331

  Anh, V V ^a   Leonenko, N N ^b   Sakhno, L M ^c  

^a QUEENSLAND UNIVERSITY OF TECHNOLOGY   (Australia)

^b CARDIFF UNIVERSITY   (United Kingdom)

^c TARAS SHEVCHENKO NATIONAL UNIVERSITY OF KYIV   (Ukraine)

Author keywords

Asymptotic normality; Consistency; Cumulant spectra; Frequency domain estimation; Long range dependence; Minimum contrast estimators

Indexed keywords

EID: 33845216050     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jspi.2006.03.001     Document Type: Article

References (34)

1. Anh V.V., Angulo J.M., and Ruiz-Medina M.D. Possible long-range dependence in fractional random fields. J. Statist. Plann. Inference 80 (1999) 95-110
2. Anh V.V., Heyde C.C., and Leonenko N.N. Dynamic models of long-range dependent processes driven by Lévy noise. J. Appl. Probab. 39 (2002) 730-747
3. Anh V.V., Leonenko N.N., Moldavskaya E.M., and Sakhno L.M. Estimation of spectral densities with multiplicative parameter. Acta Appl. Math. 79 (2003) 115-128
4. Anh V.V., Leonenko N.N., and Sakhno L.M. On a class of minimum contrast estimators for fractional stochastic processes and fields. J. Statist. Plann. Inference 123 (2004) 161-185
5. Barndorff-Nielsen O.E., and Shephard N. Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial econometrics. J. Roy. Statist. Soc. Ser. B 63 (2001) 167-241
6. Bentkus R. Cumulants of estimates of the spectrum of a stationary sequence. Liet. Mat. Rink. 16 (1976) 37-61 (in Russian)
7. Bentkus R., and Malyukyavichyus R.R. Statistical estimation of a multidimensional parameter of a spectral density. I, II. Lithuanian Math. J. 28 (1988) 115-126 415-431
8. Brillinger D.R. Introduction to polyspectra. Ann. Math. Statist. 36 (1965) 1351-1374
9. Brillinger D.R. Time Series: Data Analysis and Theory (1981), Holden Day, San Francisco
10. Brillinger D.R. Fourier inference: some methods for the analysis of array and nonGaussian series data. Water Resources Bull. 21 (1985) 743-756
11. Brillinger D.R., and Rosenblatt M. Asymptotic theory of kth order spectra. In: Harris B. (Ed). Spectral Analysis of Time Series (1967), New York, Wiley 153-188
12. Dusmuir W., and Hannan E.J. Vector linear time series models. Adv. Appl. Probab. 8 (1976) 339-360
13. Fox R., and Taqqu M.S. Large-sample properties of parameter estimates for strongly dependent stationary Gaussian time series. Ann. Statist. 14 (1986) 517-532
14. Gao J., Anh V.V., Heyde C.C., and Tieng Q. Parameter estimation of stochastic processes with long-range dependence and intermittency. J. Time Ser. Anal. 22 (2001) 517-535
15. Gao J., Anh V.V., and Heyde C.C. Statistical estimation of nonstationary Gaussian processes with long-range dependence and intermittency. Stochastics Process. Appl. 99 (2002) 295-321
16. Giraitis L., and Surgailis D. A central limit theorem for quadratic forms in strongly dependent linear variables and its application to asymptotic normality of Whittle estimate. Probab. Theory Related Fields 86 (1990) 87-104
17. Giraitis L., and Taqqu M. Whittle estimator for finite-variance non-Gaussian time series with long memory. Ann. Statist. 27 (1999) 178-203
18. Guyon X. Random Fields on a Network: Modelling, Statistics and Applications (1995), Springer, New York
19. Hannan E.J. Multiple Time Series (1970), Springer, New York
20. Hannan E.J. The asymptotic theory of linear time series models. J. Appl. Probab. 10 (1973) 130-145
21. Heyde C.C. A risky asset model with strong dependence through fractal activity time. J. Appl. Probab. 36 (1999) 1234-1239
22. Heyde C.C., and Gay R. Smoothed periodogram asymptotics and estimation for processes and fields with possible long-range dependence. Stochastics Process. Appl. 45 (1993) 169-182
23. Hosoya Y., and Taniguchi M. A central limit theorem for stationary processes and the parameter estimation of linear processes. Ann. Statist. 10 (1982) 132-153
24. Ibragimov I.A. On maximum likelihood estimation of parameters of the spectral density of stationary time series. Theory Probab. Appl. 12 (1967) 115-119
25. Keenan D.M. Asymptotic properties of minimization estimators for time series parameters. Ann. Statist. 13 (1985) 369-382
26. Keenan D.M. Limiting behavior of functionals of higher-order sample cumulant spectra. Ann. Statist. 15 (1987) 134-151
27. Leonenko N.N., Sikorskii A., and Terdik G. On a spectral and bispectral estimator of the parameter of nonGaussian data. Random. Oper. Stoch. Equations 6 (1998) 159-182 Correction: Random. Oper. Stoch. Equations 7 (1999) 107
28. Leonov V.V., and Shiryaev A.N. On a method of calculation of semi-invariants. Theory Probab. Appl. 4 (1959) 319-329
29. Ludeña. Parametric estimation for Gaussian long-range dependent processes based on the log-periodogram. Bernoulli 6 (2000) 709-728
30. Rosenblatt M.R. Stationary Sequences and Random Fields (1985), Birkhäuser, Boston
31. Taniguchi M. Minimum contrast estimation for spectral densities of stationary processes. J. Roy. Statist. Soc. B 49 (1987) 315-325
32. Terdik, G., 1999. Bilinear Stochastic Models and Related Problems on Nonlinear Time Series Analysis, Lecture Notes in Statistics, vol. 142. Springer, New York.
33. Terdik G., Dal Z., Molnar S., and Igloi E. Bispectral analysis of traffic in higher speed networks. Comput. Math. Appl. 43 (2002) 1575-1583
34. Whittle P. Hypothesis Testing in Time Series (1951), Hafner, New York