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Long and Short Memory Conditional Heteroscedasticity in Estimating the Memory Parameter of Levels - (Now published in Econometric Theory, 15 (1999), pp.299-336.)

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  • Marc Henry
  • Peter M Robinson

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 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.

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Bibliographic Info

Paper provided by Suntory and Toyota International Centres for Economics and Related Disciplines, LSE in its series STICERD - Econometrics Paper Series with number /1998/357.

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Date of creation: Aug 1998
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Handle: RePEc:cep:stiecm:/1998/357

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Web page: http://sticerd.lse.ac.uk/_new/publications/default.asp

Related research

Keywords: long memory; dynamic conditional heteroscedasticity; semiparametric estimation;

References

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  1. Nelson, Daniel B., 1990. "Stationarity and Persistence in the GARCH(1,1) Model," Econometric Theory, Cambridge University Press, vol. 6(03), pages 318-334, September.
  2. Baillie, Richard T. & Bollerslev, Tim & Mikkelsen, Hans Ole, 1996. "Fractionally integrated generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, Elsevier, vol. 74(1), pages 3-30, September.
  3. Weiss, Andrew A., 1986. "Asymptotic Theory for ARCH Models: Estimation and Testing," Econometric Theory, Cambridge University Press, vol. 2(01), pages 107-131, April.
  4. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers, Toulouse - GREMAQ 95.400, Toulouse - GREMAQ.
  5. Lo, Andrew W, 1991. "Long-Term Memory in Stock Market Prices," Econometrica, Econometric Society, Econometric Society, vol. 59(5), pages 1279-313, September.
  6. Lee, Sang-Won & Hansen, Bruce E., 1994. "Asymptotic Theory for the Garch(1,1) Quasi-Maximum Likelihood Estimator," Econometric Theory, Cambridge University Press, vol. 10(01), pages 29-52, March.
  7. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, Elsevier, vol. 31(3), pages 307-327, April.
  8. Paolo Zaffaroni & Peter M. Robinson, 1997. "Nonlinear Time Series With Long Memory: A Model for Stochastic Volatility," FMG Discussion Papers, Financial Markets Group dp253, Financial Markets Group.
  9. Richard Payne & Marc Henry, 1997. "An Investigation of Long Range Dependence in Intra-Day Foreign Exchange Rate Volatility," FMG Discussion Papers, Financial Markets Group dp264, Financial Markets Group.
  10. Robinson, P. M., 1991. "Testing for strong serial correlation and dynamic conditional heteroskedasticity in multiple regression," Journal of Econometrics, Elsevier, Elsevier, vol. 47(1), pages 67-84, January.
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Citations

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Cited by:
  1. Robinson, Peter M. & Henry, Marc, 2003. "Higher-order kernel semiparametric M-estimation of long memory," Journal of Econometrics, Elsevier, Elsevier, vol. 114(1), pages 1-27, May.
  2. Derek Bond & Michael J. Harrison & Niall Hession & Edward J. O'Brien, 2006. "Some Empirical Observations on the Forward Exchange Rate Anomaly," Trinity Economics Papers, Trinity College Dublin, Department of Economics tep2006, Trinity College Dublin, Department of Economics.
  3. Afonso Goncalves da Silva & Peter Robinson, 2008. "Finite Sample Performance in Cointegration Analysis of Nonlinear Time Series with Long Memory," Econometric Reviews, Taylor & Francis Journals, Taylor & Francis Journals, vol. 27(1-3), pages 268-297.
  4. Jonathan Wright, 2002. "Log-Periodogram Estimation Of Long Memory Volatility Dependencies With Conditionally Heavy Tailed Returns," Econometric Reviews, Taylor & Francis Journals, Taylor & Francis Journals, vol. 21(4), pages 397-417.
  5. Derek Bond & Michael J. Harrison & Edward J. O'Brien, 2006. "Purchasing Power Parity: The Irish Experience Re-visited," Trinity Economics Papers, Trinity College Dublin, Department of Economics tep200615, Trinity College Dublin, Department of Economics.
  6. Liudas Giraitis & Peter M Robinson, 2002. "Edgeworth Expansions for Semiparametric Whittle Estimation of Long Memory," STICERD - Econometrics Paper Series, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE /2002/438, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.

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