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A central limit theorem for quadratic forms in strongly dependent linear variables and its application to asymptotical normality of Whittle's estimate
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  • Published: March 1990

A central limit theorem for quadratic forms in strongly dependent linear variables and its application to asymptotical normality of Whittle's estimate

  • L. Giraitis1 &
  • D. Surgailis1 

Probability Theory and Related Fields volume 86, pages 87–104 (1990)Cite this article

Summary

A central limit theorem for quadratic forms in strongly dependent linear (or moving average) variables is proved, generalizing the results of Avram [1] and Fox and Taqqu [3] for Gaussian variables. The theorem is applied to prove asymptotical normality of Whittle's estimate of the parameter of strongly dependent linear sequences.

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References

  1. Avram, F.: On bilinear forms in Gaussian random variables and Toeplitz matrices. Probab. Th. Rel. Fields79, 37–45 (1988)

    Google Scholar 

  2. Dahlhaus, R.: Efficient parameter estimation for self-similar processes. Ann. Stat.17, 1749–1766 (1989)

    Google Scholar 

  3. Fox, R., Taqqu, M.S.: Central limit theorems for quadratic forms in random variables having long-range dependence. Probab. Th. Rel. Fields74, 213–240 (1987)

    Google Scholar 

  4. Fox, R., Taqqu, M.S.: Large sample properties of parameter estimates for strongly dependent stationary Gaussian time series. Ann. Statist.14, 517–532 (1986)

    Google Scholar 

  5. Grenander, V., Szegő, G.: Toeplitz forms and their applications. University of California Press 1958

  6. Hannan, E.J.: The asymptotic theory of linear time series models. J. Appl. Probab.10, 130–145 (1973)

    Google Scholar 

  7. Ibragimov, I.A., Linnik, J.V.: Independent and stationary sequences of random variables. Gröningen: Walters-Noordhoff 1971

    Google Scholar 

  8. Natanson, I.P.: Theory of functions of a real variable, vol. I. New York: Ungar 1955

    Google Scholar 

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Authors and Affiliations

  1. Institute of Mathematics and Cybernetics, SU-232600, Vilnius, Lithuania

    L. Giraitis & D. Surgailis

Authors
  1. L. Giraitis
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  2. D. Surgailis
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Giraitis, L., Surgailis, D. A central limit theorem for quadratic forms in strongly dependent linear variables and its application to asymptotical normality of Whittle's estimate. Probab. Th. Rel. Fields 86, 87–104 (1990). https://doi.org/10.1007/BF01207515

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  • Received: 18 January 1989

  • Revised: 15 February 1990

  • Issue Date: March 1990

  • DOI: https://doi.org/10.1007/BF01207515

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Keywords

  • Stochastic Process
  • Probability Theory
  • Quadratic Form
  • Dependent Linear
  • Limit Theorem
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