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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
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    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

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    Bibliographic Info

    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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    Postal: Lecturas de Economía, Departamento de Economía, Calle 67, 53-108, Medellin 050010, Colombia.

    Related research

    Keywords: Hypothesis testing; time-series models;

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    1. 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.
    2. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
    3. Tanaka, Katsuto, 1999. "The Nonstationary Fractional Unit Root," Econometric Theory, Cambridge University Press, vol. 15(04), pages 549-582, August.
    4. 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.
    5. Lo, Andrew W, 1991. "Long-Term Memory in Stock Market Prices," Econometrica, Econometric Society, vol. 59(5), pages 1279-313, September.
    6. Hauser, Michael A, 1997. "Semiparametric and Nonparametric Testing for Long Memory: A Monte Carlo Study," Empirical Economics, Springer, vol. 22(2), pages 247-71.
    7. Harris, David & McCabe, Brendan & Leybourne, Stephen, 2008. "Testing For Long Memory," Econometric Theory, Cambridge University Press, vol. 24(01), pages 143-175, February.
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