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Minimum distance estimation of stationary and non-stationary ARFIMA processes

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  • Laura Mayoral

Abstract

A new parametric minimum distance time-domain estimator for ARFIMA processes is introduced in this paper. The proposed estimator minimizes the sum of squared correlations of residuals obtained after filtering a series through ARFIMA parameters. The estimator is easy to compute and is consistent and asymptotically normally distributed for fractionally integrated (FI) processes with an integration order d strictly greater than -0.75. Therefore, it can be applied to both stationary and non-stationary processes. Deterministic components are also allowed in the DGP. Furthermore, as a by-product, the estimation procedure provides an immediate check on the adequacy of the specified model. This is so because the criterion function, when evaluated at the estimated values, coincides with the Box-Pierce goodness of fit statistic. Empirical applications and Monte-Carlo simulations supporting the analytical results and showing the good performance of the estimator in finite samples are also provided.

Suggested Citation

  • Laura Mayoral, 2006. "Minimum distance estimation of stationary and non-stationary ARFIMA processes," Economics Working Papers 959, Department of Economics and Business, Universitat Pompeu Fabra.
  • Handle: RePEc:upf:upfgen:959
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    References listed on IDEAS

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    1. 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.
    2. Peter C.B. Phillips, 1999. "Discrete Fourier Transforms of Fractional Processes," Cowles Foundation Discussion Papers 1243, Cowles Foundation for Research in Economics, Yale University.
    3. Chen, Willa W. & Deo, Rohit S., 2004. "A Generalized Portmanteau Goodness-Of-Fit Test For Time Series Models," Econometric Theory, Cambridge University Press, vol. 20(02), pages 382-416, April.
    4. Hong, Yongmiao, 1996. "Consistent Testing for Serial Correlation of Unknown Form," Econometrica, Econometric Society, vol. 64(4), pages 837-864, July.
    5. Michelacci, Claudio & Zaffaroni, Paolo, 2000. "(Fractional) beta convergence," Journal of Monetary Economics, Elsevier, vol. 45(1), pages 129-153, February.
    6. Tanaka, Katsuto, 1999. "The Nonstationary Fractional Unit Root," Econometric Theory, Cambridge University Press, vol. 15(04), pages 549-582, August.
    7. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
    8. Juan J. Dolado & Jesús Gonzalo & Laura Mayoral, 2005. "Testing I(1) against I(d) alternatives in the presence of deteministic components," Economics Working Papers 957, Department of Economics and Business, Universitat Pompeu Fabra.
    9. 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.
    10. Chung, C.F. & Schmidt, P., 1994. "The Minimum Distance Estimator for Fractionally Integrated ARMA Models," Papers 9408, Michigan State - Econometrics and Economic Theory.
    11. Sowell, Fallaw, 1990. "The Fractional Unit Root Distribution," Econometrica, Econometric Society, vol. 58(2), pages 495-505, March.
    12. Hosking, Jonathan R. M., 1996. "Asymptotic distributions of the sample mean, autocovariances, and autocorrelations of long-memory time series," Journal of Econometrics, Elsevier, vol. 73(1), pages 261-284, July.
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    Citations

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    Cited by:

    1. Baillie, Richard T. & Kapetanios, George & Papailias, Fotis, 2014. "Bandwidth selection by cross-validation for forecasting long memory financial time series," Journal of Empirical Finance, Elsevier, vol. 29(C), pages 129-143.
    2. Guglielmo Maria Caporale & Luis Gil‐Alana, 2014. "Long‐Run and Cyclical Dynamics in the US Stock Market," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 33(2), pages 147-161, March.
    3. Zevallos, Mauricio & Palma, Wilfredo, 2013. "Minimum distance estimation of ARFIMA processes," Computational Statistics & Data Analysis, Elsevier, vol. 58(C), pages 242-256.
    4. Guglielmo Caporale & Luis Gil-Alana, 2013. "Long memory in US real output per capita," Empirical Economics, Springer, vol. 44(2), pages 591-611, April.
    5. Baillie, Richard T. & Kapetanios, George & Papailias, Fotis, 2014. "Modified information criteria and selection of long memory time series models," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 116-131.
    6. Terence Tai-Leung Chong, 2007. "Estimating the Fractionally Integrated Model with a Break in the Differencing Parameter," Economics Bulletin, AccessEcon, vol. 3(67), pages 1-10.
    7. Juan F. Jimeno & Esther Moral & Lorena Saiz, 2006. "Structural breaks in labor productivity growth: the United States vs. the European Union," Working Papers 0625, Banco de España;Working Papers Homepage.
    8. repec:ebl:ecbull:v:3:y:2007:i:67:p:1-10 is not listed on IDEAS
    9. Beran, Jan & Ghosh, Sucharita & Schell, Dieter, 2009. "On least squares estimation for long-memory lattice processes," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2178-2194, November.

    More about this item

    Keywords

    Fractional integration; nonstationary long-memory time series; minimum distance estimation;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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