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Non-Gaussian Log-Periodogram Regression

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  • Velasco, Carlos

Abstract

We show the consistency of the log-periodogram regression estimate of the long memory parameter for long range dependent linear, not necessarily Gaussian, time series when we make a pooling of periodogram ordinates. Then, we study the asymptotic behavior of the tapered periodogram of long range dependent time series for frequencies near the origin, and we obtain the asymptotic distribution of the log-periodogram estimate for possibly non-Gaussian observation when the tapered periodogram is used. For these results we rely on higher order asymptotic properties of a vector of periodogram ordinates of the linear innovations. Finally, we assess the validity of the asymptotic results for finite samples via Monte Carlo simulation.

Suggested Citation

  • Velasco, Carlos, 2000. "Non-Gaussian Log-Periodogram Regression," Econometric Theory, Cambridge University Press, vol. 16(1), pages 44-79, February.
    • Handle: RePEc:cup:etheor:v:16:y:2000:i:01:p:44-79_16
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    1. Clifford M. Hurvich & Bonnie K. Ray, 1995. "Estimation Of The Memory Parameter For Nonstationary Or Noninvertible Fractionally Integrated Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 16(1), pages 17-41, January.
    2. Robinson, P. M., 1986. "On the errors-in-variables problem for time series," Journal of Multivariate Analysis, Elsevier, vol. 19(2), pages 240-250, August.
    3. Rainer Sachs, 1994. "Estimating non-linear functions of the spectral density, using a data-taper," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(3), pages 453-474, September.
    4. Lobato, I. & Robinson, P. M., 1996. "Averaged periodogram estimation of long memory," Journal of Econometrics, Elsevier, vol. 73(1), pages 303-324, July.
    5. Chen Zhao‐Guo & E. J. Hannan, 1980. "The Distribution Of Periodogram Ordinates," Journal of Time Series Analysis, Wiley Blackwell, vol. 1(1), pages 73-82, January.
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