On the Whittle estimators for some classes of continuous-parameter random processes and fields

Statistics and Probability Letters

Volumn 76, Issue 8, 2006, Pages 781-795

  Leonenko, N N ^a   Sakhno, L M ^b  

^a CARDIFF UNIVERSITY   (United Kingdom)

^b TARAS SHEVCHENKO NATIONAL UNIVERSITY OF KYIV   (Ukraine)

Author keywords

Asymptotic normality; Consistency; Minimum contrast estimators; Whittle estimators

Indexed keywords

EID: 33644923219     PISSN: 01677152     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spl.2005.10.010     Document Type: Article

References (35)

1. V.V. Anh J.M. Angulo M.D. Ruiz-Medina Possible long-range dependence in fractional random fields J. Statist. Plann. Infer. 80 1/2 1999 95-110
2. V.V. Anh N.N. Leonenko R. McVinish Models for fractional Riesz-Bessel motion and related processes Fractals 9 3 2001 329-346
3. V.V. Anh C.C. Heyde N.N. Leonenko Dynamic models of long-memory processes driven by Lévy noise J. Appl. Probab. 39 4 2002 730-747
4. Anh, V.V., Leonenko, N.N., Sakhno, L.M., 2002b. Minimum contrast estimation of random processes based on information of the second and third orders. J. Stat. Plan. Infer, under revision.
5. V.V. Anh N.N. Leonenko L.M. Sakhno On a class of minimum contrast estimators for fractional stochastic processes and fields J. Statist. Plann. Inference 123 1 2004 161-185
6. Anh, V.V., Leonenko, N.N., Sakhno, L.M., 2004b. Quasi-likelihood-based higher-order spectral estimation of random fields with possible long-range dependence. J. Appl. Probab. 41A, Spec. Issue, 35-53.
7. R. Bentkus On the error of the estimate of the spectral function of a stationary process Liet. Mat. Rink. 12 1 1972 55-71
8. R. Bentkus Asymptotic normality of an estimate of the spectral function Litovsk. Mat. Sb. 12 3 1972 5-18
9. R. Bentkus Cumulants of estimates of the spectrum of a stationary sequence Liet. Mat. Rink. 16 4 1976 37-61
10. R.Yu. Bentkus R.R. Maliukevicius Statistical estimation of a multidimensional parameter of a spectral density, I Lithuanian Math. J. 28 2 1988 115-126
11. R.Yu. Bentkus R.R. Maliukevicius Statistical estimation of a multidimensional parameter of a spectral density, II Lithuanian Math. J. 28 3 1988 209-221
12. F. Comte E. Renault Long memory in continuous-time stochastic volatility models Math. Finance 8 4 1998 291-323
13. R. Dahlhaus Efficient parameter estimation for self-similar processes Ann. Statist. 17 1989 1749-1766
14. W. Dunsmuir E.J. Hannan Vector linear time series models Adv. Appl. Probab. 8 1976 339-360
15. R. Fox M.S. Taqqu Large-sample properties of parameter estimates for strongly dependent stationary Gaussian time series Ann. Statist. 14 2 1986 517-532
16. R. Fox M.S. Taqqu Central limit theorems for quadratic forms in random variables having long-range dependence Probab. Theory Related Fields 74 1987 213-240
17. J. Gao Modelling long-range-dependent Gaussian processes with application in continuous-time financial models J. Appl. Probab. 41 2004 467-482
18. J. Gao V.V. Anh C.C. Heyde Q. Tieng Parameter estimation of stochastic processes with long-range dependence and intermittency J. Time Series Anal. 22 2001 517-535
19. J. Gao V.V. Anh C.C. Heyde Statistical estimation of nonstationary Gaussian process with long-range dependence and intermittency Stochastic Process. Appl. 99 2002 295-321
20. M.S. Ginovian On Toeplittz type quadratic functionals of stationary Gaussian processes Probab. Theory Related Fields 100 3 1994 395-406
21. L. Giraitis D. Surgailis 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
22. L. Giraitis M. Taqqu Whittle estimator for finite-variance non-Gaussian time series with long memory Ann. Statist. 27 1 1999 178-203
23. X. Guyon Parameter estimation for a stationary process on a d-dimensional lattice Biometrica 69 1982 95-105
24. X. Guyon Random Fields on a Network Modelling, Statistics and Applications 1995 Springer New York
25. E.J. Hannan Multiple Time Series 1970 Springer New York
26. E.J. Hannan The asymptotic theory of linear time series models J. Appl. Probab. 10 1973 130-145
27. C. Heyde R. Gay On asymptotic quasi-likelihood Stochastic Process. Appl. 31 1989 223-236
28. C. Heyde R. Gay Smoothed periodogram asymptotics and estimation for processes and fields with possible long-range dependence Stochastic Process. Appl. 45 1993 169-182
29. A.V. Ivanov N.N. Leonenko Statistical Analysis of Random Fields 1989 Kluwer Dordrecht
30. N.N. Leonenko W.A. Woyczynski Parameter identification for singular random fields arising in Burgers turbulence J. Statist. Plann. Inference 80 1999 1-13
31. N.N. Leonenko W.A. Woyczynski Parameter identification for stochastic Burgers' flows via parabolic rescaling Probab. Math. Statist. 21 1 2001 1-55
32. V.V. Leonov A.N. Shiryaev On a method of calculation of semi-invariants Theoret. Probab. Appl. 4 1959 319-329
33. M.R. Rosenblatt Stationary Sequences and Random Fields 1985 Birkhäuser Boston, MA
34. P. Whittle Hypothesis Testing in Time Series 1951 Hafner New York
35. P. Whittle Estimation and information in stationary time series Ark. Mat. 2 1953 423-434