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Estimation Biases, Size and Power of a Test on the Long Memory Parameter in ARFIMA Models

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  • Elkin Castaño
  • Santiago Gallón
  • Karoll Gómez

Abstract

Castaño et al. (2008) proposed a test to investigate the existence of long memory based on the fractional differencing parameter of an ARFIMA (p, d, q) model. They showed that using an autoregressive approximation with order equal to the nearest integer of p* = T1/3 for the short-term component of this model, the test for the short memory null hypothesis against the long memory alternative hypothesis has greater power than other long memory tests, and also has an adequate size. We studied the estimation bias generated on d, and the effect on the power and size of the test when the short-term component is ignored and when the used models do not approximate it adequately. Additionally we analyze whether the obtained results by Castaño et al. (2008) can be improved employing a different autoregressive approximation

Suggested Citation

  • Elkin Castaño & Santiago Gallón & Karoll Gómez, 2010. "Estimation Biases, Size and Power of a Test on the Long Memory Parameter in ARFIMA Models," Lecturas de Economía, Universidad de Antioquia, Departamento de Economía, issue 73, pages 131-148.
  • Handle: RePEc:lde:journl:y:2010:i:73:p:131-148
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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. Granger, C. W. J., 1980. "Long memory relationships and the aggregation of dynamic models," Journal of Econometrics, Elsevier, vol. 14(2), pages 227-238, October.
    3. Lo, Andrew W, 1991. "Long-Term Memory in Stock Market Prices," Econometrica, Econometric Society, vol. 59(5), pages 1279-1313, September.
    4. Harris, David & McCabe, Brendan & Leybourne, Stephen, 2008. "Testing For Long Memory," Econometric Theory, Cambridge University Press, vol. 24(01), pages 143-175, February.
    5. Hauser, Michael A, 1997. "Semiparametric and Nonparametric Testing for Long Memory: A Monte Carlo Study," Empirical Economics, Springer, vol. 22(2), pages 247-271.
    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.
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    More about this item

    Keywords

    Hypothesis testing; time-series models;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: 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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