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An alternative maximum likelihood estimator of long-memory processes using compactly supported wavelets

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  • Jensen, Mark J.

Abstract

In this paper we apply compactly supported wavelets to the ARFIMA(p,d,q) long-memory process to develop an alternative maximum likelihood estimator of the differencing parameter, d, that is invariant to the unknown mean and model specification, and to the level of contamination. We show that this class of time series have wavelet transforms who's covariance matrix is sparse when the wavelet is compactly supported. It is shown that the sparse covariance matrix can be approximated to a high level of precision by a matix equal to the covariance amtrix except with the off-diagonal elements set to zero. This diagonal matrix is shown to reduce the order of calculating the likelihood function to an order smaller than those associated with the exact MLE method. We test the robustness of the wavelet MLE of the fractional differencing parameter to a variety of compactly supported wavelets, series length, and contamination by generating ARFIMA(p,d,q) processes for different values of p, d, and q and calculating the wavelet MLE estimate using only the main diagonal elements of its covariance matrix. In our simulations we find the wavelet MLE to be superior to the approximate MLE when estimating contaminated ARFIMA(0,d,0), and uncontaminated ARFIMA(1,d,0) and ARFIMA(0,d,1) processes except when the MA parameter is close to one. We also find the wavelet MLE to be robust to model specification and as such is an attractive alternative semiparametric estimator to the Geweke-Hudak estimator.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Dynamics and Control.

Volume (Year): 24 (2000)
Issue (Month): 3 (March)
Pages: 361-387

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Handle: RePEc:eee:dyncon:v:24:y:2000:i:3:p:361-387

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References

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  1. Mark J. Jensen, 1997. "Using Wavelets to Obtain a Consistent Ordinary Least Squares Estimator of the Long Memory Parameter," Econometrics 9710002, EconWPA.
  2. Cheung, Yin-Wong & Diebold, Francis X., 1994. "On maximum likelihood estimation of the differencing parameter of fractionally-integrated noise with unknown mean," Journal of Econometrics, Elsevier, vol. 62(2), pages 301-316, June.
  3. repec:wop:humbsf:1995-8 is not listed on IDEAS
  4. Breidt, F. Jay & Crato, Nuno & de Lima, Pedro, 1998. "The detection and estimation of long memory in stochastic volatility," Journal of Econometrics, Elsevier, vol. 83(1-2), pages 325-348.
  5. 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.
  6. C. M. Schmidt & R. Tschernig, 1995. "The Identification of Fractional ARIMA Models," SFB 373 Discussion Papers 1995,8, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  7. 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.
  8. Alex Maynard & Peter C. B. Phillips, 2001. "Rethinking an old empirical puzzle: econometric evidence on the forward discount anomaly," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(6), pages 671-708.
  9. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
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Citations

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Cited by:
  1. Crowley, Patrick, 2005. "An intuitive guide to wavelets for economists," Research Discussion Papers 1/2005, Bank of Finland.
  2. Morten Ørregaard Nielsen & Per Frederiksen, 2005. "Finite Sample Comparison of Parametric, Semiparametric, and Wavelet Estimators of Fractional Integration," Working Papers 1189, Queen's University, Department of Economics.
  3. Fernandez, Viviana, 2010. "Commodity futures and market efficiency: A fractional integrated approach," Resources Policy, Elsevier, vol. 35(4), pages 276-282, December.
  4. Collet J.J. & Fadili J.M., 2005. "Simulation of Gegenbauer processes using wavelet packets," School of Economics and Finance Discussion Papers and Working Papers Series 190, School of Economics and Finance, Queensland University of Technology.
  5. Bae, Sang-Kun & Jensen, Mark J. & Murdock, Scott G., 2005. "Long-run neutrality in a fractionally integrated model," Journal of Macroeconomics, Elsevier, vol. 27(2), pages 257-274, June.
  6. Michis, Antonis A., 2014. "Time scale evaluation of economic forecasts," Economics Letters, Elsevier, vol. 123(3), pages 279-281.
  7. In, Francis & Kim, Sangbae, 2006. "Multiscale hedge ratio between the Australian stock and futures markets: Evidence from wavelet analysis," Journal of Multinational Financial Management, Elsevier, vol. 16(4), pages 411-423, October.
  8. In, Francis & Kim, Sangbae & Gençay, Ramazan, 2011. "Investment horizon effect on asset allocation between value and growth strategies," Economic Modelling, Elsevier, vol. 28(4), pages 1489-1497, July.
  9. Carla Ysusi, 2009. "Analysis of the Dynamics of Mexican Inflation Using Wavelets," Working Papers 2009-09, Banco de México.
  10. In, Francis & Kim, Sangbae, 2007. "A note on the relationship between Fama-French risk factors and innovations of ICAPM state variables," Finance Research Letters, Elsevier, vol. 4(3), pages 165-171, September.
  11. Jensen Mark J., 1999. "An Approximate Wavelet MLE of Short- and Long-Memory Parameters," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 3(4), pages 1-17, January.
  12. Tan, Pei P. & Galagedera, Don U.A. & Maharaj, Elizabeth A., 2012. "A wavelet based investigation of long memory in stock returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(7), pages 2330-2341.
  13. Alper Ozun & Atilla Cifter, 2008. "Modeling long-term memory effect in stock prices: A comparative analysis with GPH test and Daubechies wavelets," Studies in Economics and Finance, Emerald Group Publishing, vol. 25(1), pages 38-48, March.
  14. Jin Lee, 2000. "One-Sided Testing for ARCH Effect Using Wavelets," Econometric Society World Congress 2000 Contributed Papers 1214, Econometric Society.
  15. Vuorenmaa , Tommi, 2005. "A wavelet analysis of scaling laws and long-memory in stock market volatility," Research Discussion Papers 27/2005, Bank of Finland.
  16. SangKun Bae & Mark J. Jensen, 1998. "Long-Run Neutrality in a Long-Memory Model," Macroeconomics 9809006, EconWPA, revised 30 Sep 1998.
  17. Haven, Emmanuel & Liu, Xiaoquan & Shen, Liya, 2012. "De-noising option prices with the wavelet method," European Journal of Operational Research, Elsevier, vol. 222(1), pages 104-112.
  18. Heni Boubaker & Nadia Sghaier, 2014. "Wavelet based Estimation of Time- Varying Long Memory Model with Nonlinear Fractional Integration Parameter," Working Papers 2014-284, Department of Research, Ipag Business School.

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