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Minimum distance estimation of k-factors GARMA processes

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  • Kouamé, Euloge F.
  • Hili, Ouagnina

Abstract

We consider minimum distance estimation of k-factors Gegenbauer Autoregressive Moving Average (k-GARMA) processes. The proposed estimator minimizes the sum of squared correlations of residuals obtained after filtering a series through k-GARMA parameters. We establish the consistency of the estimator. When the k frequencies are unknown, asymptotic distribution theory for parameters estimators including the long memory parameters is significantly harder. We discuss the (non-standard) limiting distributional behavior of the estimators of k. And for the remaining parameter estimator, we establish asymptotic normality.

Suggested Citation

  • Kouamé, Euloge F. & Hili, Ouagnina, 2008. "Minimum distance estimation of k-factors GARMA processes," Statistics & Probability Letters, Elsevier, vol. 78(18), pages 3254-3261, December.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:18:p:3254-3261
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    References listed on IDEAS

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    1. Chung, Ching-Fan, 1996. "Estimating a generalized long memory process," Journal of Econometrics, Elsevier, vol. 73(1), pages 237-259, July.
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    5. Liudas Giraitis & Javier Hidalgo & Peter M Robinson, 2001. "Gaussian Estimation of Parametric Spectral Density with Unknown Pole," STICERD - Econometrics Paper Series 424, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    6. Henry L. Gray & Nien‐Fan Zhang & Wayne A. Woodward, 1989. "On Generalized Fractional Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 10(3), pages 233-257, May.
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    1. Richard Hunt & Shelton Peiris & Neville Weber, 2022. "Estimation methods for stationary Gegenbauer processes," Statistical Papers, Springer, vol. 63(6), pages 1707-1741, December.
    2. Zevallos, Mauricio & Palma, Wilfredo, 2013. "Minimum distance estimation of ARFIMA processes," Computational Statistics & Data Analysis, Elsevier, vol. 58(C), pages 242-256.

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