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

  • Elkin Castaño
  • Santiago Gallón
  • Karoll Gómez
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    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

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    Article provided by Universidad de Antioquia, Departamento de Economía in its journal LECTURAS DE ECONOMÍA.

    Volume (Year): (2010)
    Issue (Month): 73 ()
    Pages: 131-148

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    Handle: RePEc:lde:journl:y:2010:i:73:p:131-148
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    1. Lo, Andrew W. (Andrew Wen-Chuan), 1989. "Long-term memory in stock market prices," Working papers 3014-89., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    2. Tanaka, Katsuto, 1999. "The Nonstationary Fractional Unit Root," Econometric Theory, Cambridge University Press, vol. 15(04), pages 549-582, August.
    3. Harris, David & McCabe, Brendan & Leybourne, Stephen, 2008. "Testing For Long Memory," Econometric Theory, Cambridge University Press, vol. 24(01), pages 143-175, February.
    4. 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.
    5. Hauser, Michael A, 1997. "Semiparametric and Nonparametric Testing for Long Memory: A Monte Carlo Study," Empirical Economics, Springer, vol. 22(2), pages 247-71.
    6. 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.
    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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