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The integrated periodogram for long-memory processes with finite or infinite variance

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  • Kokoszka, P.
  • Mikosch, T.

Abstract

We derive functional limit theorems for the integrated periodogram of linear processes whose innovations may have finite or infinite variance, and which may exhibit long memory. The results are applied to obtain corresponding Kolmogorov-Smirnov and Cramér-von Mises goodness-of-fit tests.

Suggested Citation

  • Kokoszka, P. & Mikosch, T., 1997. "The integrated periodogram for long-memory processes with finite or infinite variance," Stochastic Processes and their Applications, Elsevier, vol. 66(1), pages 55-78, February.
    • Handle: RePEc:eee:spapps:v:66:y:1997:i:1:p:55-78
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    References listed on IDEAS

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    1. Dahlhaus, Rainer, 1988. "Empirical spectral processes and their applications to time series analysis," Stochastic Processes and their Applications, Elsevier, vol. 30(1), pages 69-83, November.
    2. Mikosch, T., 1991. "Functional limit theorems for random quadratic forms," Stochastic Processes and their Applications, Elsevier, vol. 37(1), pages 81-98, February.
    3. Dahlhaus, Rainer, 1985. "Asymptotic normality of spectral estimates," Journal of Multivariate Analysis, Elsevier, vol. 16(3), pages 412-431, June.
    4. Kokoszka, Piotr S. & Taqqu, Murad S., 1995. "Fractional ARIMA with stable innovations," Stochastic Processes and their Applications, Elsevier, vol. 60(1), pages 19-47, November.
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    Cited by:

    1. Vitalii Makogin & Marco Oesting & Albert Rapp & Evgeny Spodarev, 2021. "Long range dependence for stable random processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(2), pages 161-185, March.
    2. Li, Ming, 2017. "Record length requirement of long-range dependent teletraffic," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 472(C), pages 164-187.
    3. Yuichi Goto & Tobias Kley & Ria Van Hecke & Stanislav Volgushev & Holger Dette & Marc Hallin, 2021. "The Integrated Copula Spectrum," Working Papers ECARES 2021-29, ULB -- Universite Libre de Bruxelles.
    4. Can, S.U. & Mikosch, T. & Samorodnitsky, G., 2010. "Weak Convergence of the function-indexed integrated periodogram for infinite variance processes," Other publications TiSEM 3be90f1b-2f53-4987-b46e-c, Tilburg University, School of Economics and Management.
    5. Marinucci, D. & Robinson, P. M., 2000. "Weak convergence of multivariate fractional processes," Stochastic Processes and their Applications, Elsevier, vol. 86(1), pages 103-120, March.
    6. Bhansali, R.J. & Giraitis, L. & Kokoszka, P.S., 2007. "Approximations and limit theory for quadratic forms of linear processes," Stochastic Processes and their Applications, Elsevier, vol. 117(1), pages 71-95, January.
    7. Rademacher, Daniel & Kreiß, Jens-Peter & Paparoditis, Efstathios, 2024. "Asymptotic normality of spectral means of Hilbert space valued random processes," Stochastic Processes and their Applications, Elsevier, vol. 173(C).
    8. Kokoszka, Piotr & Mikosch, Thomas, 2000. "The periodogram at the Fourier frequencies," Stochastic Processes and their Applications, Elsevier, vol. 86(1), pages 49-79, March.
    9. Ørregaard Nielsen, Morten, 2004. "Local empirical spectral measure of multivariate processes with long range dependence," Stochastic Processes and their Applications, Elsevier, vol. 109(1), pages 145-166, January.
    10. Surgailis, Donatas, 0. "Stable limits of empirical processes of moving averages with infinite variance," Stochastic Processes and their Applications, Elsevier, vol. 100(1-2), pages 255-274, July.
    11. Peng, Liang, 2001. "Semi-parametric estimation of long-range dependence index in infinite variance time series," Statistics & Probability Letters, Elsevier, vol. 51(2), pages 101-109, January.
    12. Mikosch, T. & Norvaisa, R., 1997. "Uniform convergence of the empirical spectral distribution function," Stochastic Processes and their Applications, Elsevier, vol. 70(1), pages 85-114, October.
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    14. Fasen-Hartmann, Vicky & Mayer, Celeste, 2023. "Empirical spectral processes for stationary state space models," Stochastic Processes and their Applications, Elsevier, vol. 155(C), pages 319-354.

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