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Maximum likelihood estimation of the fractional differencing parameter in an ARFIMA model using wavelets

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  • Tse, Y.K.
  • Anh, V.V.
  • Tieng, Q.

Abstract

In this paper, we examine the finite-sample properties of the approximate maximum likelihood estimate (MLE) of the fractional differencing parameter d in an ARFIMA(p, d, q) model based on the wavelet coefficients. Ignoring wavelet coefficients of higher order of resolution, the remaining wavelet coefficients approximate a sample of independently and identically distributed normal variates with homogeneous variance within each level. The approximate MLE performs satisfactorily and provides a robust estimate for which the short memory component need not be specified.

Suggested Citation

  • Tse, Y.K. & Anh, V.V. & Tieng, Q., 2002. "Maximum likelihood estimation of the fractional differencing parameter in an ARFIMA model using wavelets," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 59(1), pages 153-161.
    • Handle: RePEc:eee:matcom:v:59:y:2002:i:1:p:153-161
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    References listed on IDEAS

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    1. Davidson, Russell & Labys, Walter C & Lesourd, Jean-Baptiste, 1998. "Wavelet Analysis of Commodity Price Behavior," Computational Economics, Springer;Society for Computational Economics, vol. 11(1-2), pages 103-128, April.
    2. Pan, Zuohong & Wang, Xiaodi, 1998. "A Stochastic Nonlinear Regression Estimator Using Wavelets," Computational Economics, Springer;Society for Computational Economics, vol. 11(1-2), pages 89-102, April.
    3. Iain M. Johnstone & Bernard W. Silverman, 1997. "Wavelet Threshold Estimators for Data with Correlated Noise," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(2), pages 319-351.
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    Cited by:

    1. Morten Ørregaard Nielsen & Per Houmann Frederiksen, 2005. "Finite Sample Comparison of Parametric, Semiparametric, and Wavelet Estimators of Fractional Integration," Econometric Reviews, Taylor & Francis Journals, vol. 24(4), pages 405-443.
    2. Han, Lili & Wu, Fangxiang & Sheng, Jie & Ding, Feng, 2012. "Two recursive least squares parameter estimation algorithms for multirate multiple-input systems by using the auxiliary model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(5), pages 777-789.
    3. Cai, Chunhao & Cheng, Xuwen & Xiao, Weilin & Wu, Xiang, 2019. "Parameter identification for mixed fractional Brownian motions with the drift parameter," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 536(C).
    4. Chen, Feiyan & Ding, Feng & Alsaedi, Ahmed & Hayat, Tasawar, 2017. "Data filtering based multi-innovation extended gradient method for controlled autoregressive autoregressive moving average systems using the maximum likelihood principle," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 132(C), pages 53-67.

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