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Long and short memory conditional heteroscedasticity in estimating the memory parameter of levels

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  • Robinson, Peter M.
  • Henry, Marc

Abstract

Semiparametric estimates of long memory seem useful in the analysis of long financial time series because they are consistent under much broader conditions than parametric estimates. However, recent large sample theory for semiparametric estimates forbids conditional heteroscedasticity. We show that a leading semiparametric estimate, the Gaussian or local Whittle one, can be consistent and have the same limiting distribution under conditional heteroscedasticity as under conditional homoscedasticity assumed by Robinson (1995a). Indeed, noting that long memory has been observed in the squares of financial time series, we allow, under regularity conditions, for conditional heteroscedasticity of the general form introduced by Robinson (1991) which may include long memory behaviour for the squares, such as the fractional noise and autoregressive fractionally integrated moving average form, as well as standard short memory ARCH and GARCH specifications.

Suggested Citation

  • Robinson, Peter M. & Henry, Marc, 1998. "Long and short memory conditional heteroscedasticity in estimating the memory parameter of levels," LSE Research Online Documents on Economics 2022, London School of Economics and Political Science, LSE Library.
  • Handle: RePEc:ehl:lserod:2022
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    References listed on IDEAS

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    1. Sims,Christopher A. (ed.), 1994. "Advances in Econometrics," Cambridge Books, Cambridge University Press, number 9780521444606.
    2. Robinson, P. M., 1991. "Testing for strong serial correlation and dynamic conditional heteroskedasticity in multiple regression," Journal of Econometrics, Elsevier, vol. 47(1), pages 67-84, January.
    3. Guido M. Kuersteiner, 1999. "Efficiency IV Estimation for Autoregressive Models with Conditional Heterogeneity," Working papers 99-08, Massachusetts Institute of Technology (MIT), Department of Economics.
    4. Sims,Christopher A. (ed.), 1994. "Advances in Econometrics," Cambridge Books, Cambridge University Press, number 9780521444590.
    5. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    6. Weiss, Andrew A., 1986. "Asymptotic Theory for ARCH Models: Estimation and Testing," Econometric Theory, Cambridge University Press, vol. 2(1), pages 107-131, April.
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    More about this item

    Keywords

    long memory; dynamic conditional heteroscedasticity; semiparametric estimation.;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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