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Long And Short Memory Conditional Heteroskedasticity In Estimating The Memory Parameter Of Levels

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  • Robinson, P.M.
  • Henry, M.

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 heteroskedasticity. We show that a leading semiparametric estimate, the Gaussian or local Whittle one, can be consistent and have the same limiting distribution under conditional heteroskedasticity as under the conditional homoskedasticity assumed by Robinson (1995, Annals of Statistics 23, 1630–61). Indeed, noting that long memory has been observed in the squares of financial time series, we allow, under regularity conditions, for conditional heteroskedasticity of the general form introduced by Robinson (1991, Journal of Econometrics 47, 67–84), which may include long memory behavior for the squares, such as the fractional noise and autoregressive fractionally integrated moving average form, and also standard short memory ARCH and GARCH specifications.

Suggested Citation

  • Robinson, P.M. & Henry, M., 1999. "Long And Short Memory Conditional Heteroskedasticity In Estimating The Memory Parameter Of Levels," Econometric Theory, Cambridge University Press, vol. 15(3), pages 299-336, June.
  • Handle: RePEc:cup:etheor:v:15:y:1999:i:03:p:299-336_15
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    1. Sims,Christopher A. (ed.), 1994. "Advances in Econometrics," Cambridge Books, Cambridge University Press, number 9780521444606, October.
    2. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    3. 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.
    4. Weiss, Andrew A., 1986. "Asymptotic Theory for ARCH Models: Estimation and Testing," Econometric Theory, Cambridge University Press, vol. 2(1), pages 107-131, April.
    5. 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.
    6. Sims,Christopher A. (ed.), 1994. "Advances in Econometrics," Cambridge Books, Cambridge University Press, number 9780521444590, October.
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    JEL classification:

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

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