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On parameter estimation for locally stationary long-memory processes

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  • Jan Beran

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    (University of Konstanz)

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    Abstract

    We consider parameter estimation for time-dependent locally stationary long-memory processes. The asymptotic distribution of an estimator based on the local infinite autoregressive representation is derived, and asymptotic formulas for the mean squared error of the estimator, and the asymptotically optimal bandwidth are obtained. In spite of long memory, the optimal bandwidth turns out to be of the order n^(-1/5) and inversely proportional to the square of the second derivative of d. In this sense, local estimation of d is comparable to regression smoothing with iid residuals.

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    File URL: http://cofe.uni-konstanz.de/Papers/dp07_13.pdf
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    Bibliographic Info

    Paper provided by Center of Finance and Econometrics, University of Konstanz in its series CoFE Discussion Paper with number 07-13.

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    Length: 30 pages
    Date of creation: 01 Dec 2007
    Date of revision:
    Handle: RePEc:knz:cofedp:0713

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    Related research

    Keywords: long memory; fractional ARIMA process; local stationarity; bandwidth selection;

    This paper has been announced in the following NEP Reports:

    References

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    1. Jan Beran & Yuanhua.Feng, 2001. "Iterative plug-in algorithms for SEMIFAR models - definition, convergence and asymptotic properties," CoFE Discussion Paper 01-11, Center of Finance and Econometrics, University of Konstanz.
    2. Kenneth Falconer & Carmen Fern�ndez, 2007. "Inference on fractal processes using multiresolution approximation," Biometrika, Biometrika Trust, vol. 94(2), pages 313-334.
    3. Diebold, Francis X. & Inoue, Atsushi, 2001. "Long memory and regime switching," Journal of Econometrics, Elsevier, vol. 105(1), pages 131-159, November.
    4. Granger, Clive W. J. & Ding, Zhuanxin, 1996. "Varieties of long memory models," Journal of Econometrics, Elsevier, vol. 73(1), pages 61-77, July.
    5. Hallin, Marc, 1978. "Mixed autoregressive-moving average multivariate processes with time-dependent coefficients," Journal of Multivariate Analysis, Elsevier, vol. 8(4), pages 567-572, December.
    6. Dahlhaus, R., 1996. "On the Kullback-Leibler information divergence of locally stationary processes," Stochastic Processes and their Applications, Elsevier, vol. 62(1), pages 139-168, March.
    7. Beran, Jan & Feng, Yuanhua, 2002. "SEMIFAR models--a semiparametric approach to modelling trends, long-range dependence and nonstationarity," Computational Statistics & Data Analysis, Elsevier, vol. 40(2), pages 393-419, August.
    8. Sébastien Van Bellegem & Rainer Dahlhaus, 2006. "Semiparametric estimation by model selection for locally stationary processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(5), pages 721-746.
    9. Hall, Peter & Hart, Jeffrey D., 1990. "Nonparametric regression with long-range dependence," Stochastic Processes and their Applications, Elsevier, vol. 36(2), pages 339-351, December.
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