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Non-Gaussian log-periodogram regression

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  • Velasco, Carlos

Abstract

We show the consistency of the log-periodogram estimate of the long memory parameter íor long range dependent linear, non necessarily Gaussian, time series when we make a pooling oí periodogram ordinates. Then, we study the asymptotic behaviour oí the tapered periodogram of long range dependent time series íor írequencies near the origin. Finally, we obtain the asymptotic distribution of the log-periodogram estimate íor possibly non-Gaussian observations when we use the tapered periodogram. For that result we rely on higher order asymptotic properties of a vector of periodogram ordinates of the linear innovations.

Suggested Citation

  • Velasco, Carlos, 1998. "Non-Gaussian log-periodogram regression," DES - Working Papers. Statistics and Econometrics. WS 4553, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:4553
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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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    Long range dependence;

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