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Broadband semiparametric estimation of the long-memory parameter by the likelihood-based FEXP approach

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  • Masaki Narukawa
  • Yasumasa Matsuda

Abstract

This paper proposes a semiparametric estimator of the long-memory parameter to fit a fractional exponential (FEXP) model by a likelihood-based approach. We establish that our proposed estimator is more efficient than the FEXP estimator proposed independently by Moulines and Soulier (1999) and Hurvuch and Brodsky (2001), and has the same asymptotic variance as the fractionally differenced autoregressive (FAR) estimator proposed by Bhansali et al. (2006) without pooling the periodogram. The Monte Carlo studies suggest that our estimator outperforms the FEXP estimator or is not inferior to the Gaussian semiparametric estimator (GSE) and will be also empirically effective in non-Gaussian processes.

Suggested Citation

  • Masaki Narukawa & Yasumasa Matsuda, 2008. "Broadband semiparametric estimation of the long-memory parameter by the likelihood-based FEXP approach," TERG Discussion Papers 239, Graduate School of Economics and Management, Tohoku University.
    • Handle: RePEc:toh:tergaa:239
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    File URL: http://hdl.handle.net/10097/55392
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    References listed on IDEAS

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    1. Sims,Christopher A. (ed.), 1994. "Advances in Econometrics," Cambridge Books, Cambridge University Press, number 9780521444606, September.
    2. Giraitis, Liudas & Robinson, Peter M. & Samarov, Alexander, 2000. "Adaptive Semiparametric Estimation of the Memory Parameter," Journal of Multivariate Analysis, Elsevier, vol. 72(2), pages 183-207, February.
    3. Clifford M. Hurvich & Julia Brodsky, 2001. "Broadband Semiparametric Estimation of the Memory Parameter of a Long‐Memory Time Series Using Fractional Exponential Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 22(2), pages 221-249, March.
    4. Ignacio N. Lobato & Peter M. Robinson, 1998. "A Nonparametric Test for I(0)," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(3), pages 475-495.
    5. Velasco, Carlos, 2000. "Non-Gaussian Log-Periodogram Regression," Econometric Theory, Cambridge University Press, vol. 16(1), pages 44-79, February.
    6. Liudas Giraitis & Peter M Robinson & Alexander Samarov, 2000. "Adaptive Semiparametric Estimation of the Memory Parameter - (Now published with revised title, Adaptive Rate-Optimal Estimation of the Memory Parameter, in Journal of Multivariate Analysis, 72 (2000)," STICERD - Econometrics Paper Series 379, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    7. Clifford M. Hurvich & Rohit S. Deo, 1999. "Plug‐in Selection of the Number of Frequencies in Regression Estimates of the Memory Parameter of a Long‐memory Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 20(3), pages 331-341, May.
    8. Clifford M. Hurvich & Eric Moulines & Philippe Soulier, 2005. "Estimating Long Memory in Volatility," Econometrica, Econometric Society, vol. 73(4), pages 1283-1328, July.
    9. Sims,Christopher A. (ed.), 1994. "Advances in Econometrics," Cambridge Books, Cambridge University Press, number 9780521444590, September.
    10. Soulier, Philippe, 2001. "Moment bounds and central limit theorem for functions of Gaussian vectors," Statistics & Probability Letters, Elsevier, vol. 54(2), pages 193-203, September.
    11. Clifford M. Hurvich & Rohit Deo & Julia Brodsky, 1998. "The mean squared error of Geweke and Porter‐Hudak's estimator of the memory parameter of a long‐memory time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 19(1), pages 19-46, January.
    12. Diebold, Francis X. & Rudebusch, Glenn D., 1991. "On the power of Dickey-Fuller tests against fractional alternatives," Economics Letters, Elsevier, vol. 35(2), pages 155-160, February.
    13. Marc Henry, 2001. "Robust Automatic Bandwidth for Long Memory," Journal of Time Series Analysis, Wiley Blackwell, vol. 22(3), pages 293-316, May.
    14. Eric Moulines & Philippe Soulier, 2000. "Data Driven Order Selection for Projection Estimator of the Spectral Density of Time Series with Long Range Dependence," Journal of Time Series Analysis, Wiley Blackwell, vol. 21(2), pages 193-218, March.
    15. Giraitis, Liudas & Robinson, Peter M. & Samarov, Alexander, 2000. "Adaptive semiparametric estimation of the memory parameter," LSE Research Online Documents on Economics 2082, London School of Economics and Political Science, LSE Library.
    16. Clifford M. Hurvich, 2001. "Model Selection for Broadband Semiparametric Estimation of Long Memory in Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 22(6), pages 679-709, November.
    17. Fay, Gilles & Soulier, Philippe, 2001. "The periodogram of an i.i.d. sequence," Stochastic Processes and their Applications, Elsevier, vol. 92(2), pages 315-343, April.
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