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Minimum distance estimation of ARFIMA processes

  • Zevallos, Mauricio
  • Palma, Wilfredo

This paper proposes a new minimum distance methodology for the estimation of ARFIMA processes with Gaussian and non-Gaussian errors. The main advantage of this method is that it allows for a computationally efficient estimation when the long-memory parameter is in the interval d∈(−12,12). Previous minimum distance estimation techniques are usually limited to the range d∈(−12,14), leaving outside the very important case of strong long memory with d∈[14,12). It is shown that the new estimator satisfies a central limit theorem and Monte Carlo experiments indicate that the proposed estimator performs very well even for small sample sizes. The methodology is illustrated with three applications. The first two examples involve real-life time series while the third application illustrates that the proposed methodology is a sound alternative for dealing with incomplete time series.

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File URL: http://www.sciencedirect.com/science/article/pii/S0167947312003088
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Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

Volume (Year): 58 (2013)
Issue (Month): C ()
Pages: 242-256

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Handle: RePEc:eee:csdana:v:58:y:2013:i:c:p:242-256
DOI: 10.1016/j.csda.2012.08.005
Contact details of provider: Web page: http://www.elsevier.com/locate/csda

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  1. Pascal Bondon & Wilfredo Palma, 2007. "A Class of Antipersistent Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(2), pages 261-273, 03.
  2. Bhardwaj, Geetesh & Swanson, Norman R., 2006. "An empirical investigation of the usefulness of ARFIMA models for predicting macroeconomic and financial time series," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 539-578.
  3. Yin-Wong Cheung & Francis X. Diebold, 1990. "On maximum-likelihood estimation of the differencing parameter of fractionally integrated noise with unknown mean," Discussion Paper / Institute for Empirical Macroeconomics 34, Federal Reserve Bank of Minneapolis.
  4. Chen, Willa W. & Hurvich, Clifford M. & Lu, Yi, 2006. "On the Correlation Matrix of the Discrete Fourier Transform and the Fast Solution of Large Toeplitz Systems for Long-Memory Time Series," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 812-822, June.
  5. Laura Mayoral, 2007. "Minimum distance estimation of stationary and non-stationary ARFIMA processes," Econometrics Journal, Royal Economic Society, vol. 10(1), pages 124-148, 03.
  6. Doornik, Jurgen A. & Ooms, Marius, 2003. "Computational aspects of maximum likelihood estimation of autoregressive fractionally integrated moving average models," Computational Statistics & Data Analysis, Elsevier, vol. 42(3), pages 333-348, March.
  7. Lobato, Ignacio N & Velasco, Carlos, 2000. "Long Memory in Stock-Market Trading Volume," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(4), pages 410-27, October.
  8. Tieslau, Margie A. & Schmidt, Peter & Baillie, Richard T., 1996. "A minimum distance estimator for long-memory processes," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 249-264.
  9. Sowell, Fallaw, 1992. "Maximum likelihood estimation of stationary univariate fractionally integrated time series models," Journal of Econometrics, Elsevier, vol. 53(1-3), pages 165-188.
  10. 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.
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