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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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

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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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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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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

Zhuanxin Ding & Clive W.J. Granger, 1994. "Modeling Volatility Persistence of Speculative Returns: A New Approach," University of California at San Diego, Economics Working Paper Series 94-05, Department of Economics, UC San Diego.
Other versions:
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Paolo Zaffaroni & Peter M. Robinson, 1997. "Nonlinear Time Series With Long Memory: A Model for Stochastic Volatility," FMG Discussion Papers dp253, Financial Markets Group. [Downloadable!] (restricted)
Zhuanxin Ding & Clive Granger & Robert Engle, 1992. "A Long Memory Property of Stock Market Returns and a New Model," University of California at San Diego, Economics Working Paper Series 92-21, Department of Economics, UC San Diego.
Other versions:
- Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June. [Downloadable!] (restricted)
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. [Downloadable!] (restricted)
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. [Downloadable!]
Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
Other versions:
- Ghysels, E. & Harvey, A. & Renault, E., 1996. "Stochastic Volatility," Cahiers de recherche 9613, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
- Ghysels, E. & Harvey, A. & Renault, E., 1996. "Stochastic Volatility," Cahiers de recherche 9613, Universite de Montreal, Departement de sciences economiques. [Downloadable!]
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Lo, Andrew W, 1991. "Long-Term Memory in Stock Market Prices," Econometrica, Econometric Society, vol. 59(5), pages 1279-313, September. [Downloadable!] (restricted)
Other versions:
- Andrew W. Lo, 1989. "Long-term Memory in Stock Market Prices," NBER Working Papers 2984, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

Jonathan H. Wright, 2000. "Log-periodogram estimation of long memory volatility dependencies with conditionally heavy tailed returns," International Finance Discussion Papers 685, Board of Governors of the Federal Reserve System (U.S.). [Downloadable!]
Other versions:
- Jonathan Wright, 2002. "Log-Periodogram Estimation Of Long Memory Volatility Dependencies With Conditionally Heavy Tailed Returns," Econometric Reviews, Taylor and Francis Journals, vol. 21(4), pages 397-417. [Downloadable!] (restricted)
Derek Bond & Michael J. Harrison & Niall Hession & Edward J. O'Brien, 2006. "Some Empirical Observations on the Forward Exchange Rate Anomaly," Trinity Economics Papers tep2006, Trinity College Dublin, Department of Economics. [Downloadable!]
Other versions:
- Bond, Derek & Harrison, Michael J & Hession, Niall & O’Brien, Edward J., 2006. "Some Empirical Observations on the Forward Exchange Rate Anomaly," Research Technical Papers 3/RT/06, Central Bank & Financial Services Authority of Ireland (CBFSAI). [Downloadable!]
Marc Henry & Peter M Robinson, 2002. "Higher-Order Kernel Semiparametric M-Estimation of Long Memory," STICERD - Econometrics Paper Series /2002/436, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
Other versions:
- Robinson, Peter M. & Henry, Marc, 2003. "Higher-order kernel semiparametric M-estimation of long memory," Journal of Econometrics, Elsevier, vol. 114(1), pages 1-27, May. [Downloadable!] (restricted)
M. Ooms & J.A. Doornik, 1999. "Inference and forecasting for fractional autoregressive integrated moving average models; with an application to US and UK inflation," Econometric Institute Report 171, Erasmus University Rotterdam, Econometric Institute. [Downloadable!]
Other versions:
- Ooms, M. & Doornik, J.A., 1999. "Inference and forecasting for fractional autoregressive integrated moving average models; with an application to US and UK inflation," Econometric Institute Report ometric Institute Reports, Erasmus University Rotterdam, Econometric Institute. [Downloadable!]
Afonso Gonçalves da Silva & Peter M Robinson, 2006. "Finite Sample Performance in CointegrationAnalysis of Nonlinear Time Series with LongMemory," STICERD - Econometrics Paper Series /2006/501, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
Other versions:
- Afonso Gonçalves da Silva & Peter Robinson, 2008. "Finite Sample Performance in Cointegration Analysis of Nonlinear Time Series with Long Memory," Econometric Reviews, Taylor and Francis Journals, vol. 27(1-3), pages 268-297. [Downloadable!] (restricted)
Derek Bond & Michael J. Harrison & Edward J. O'Brien, 2006. "Purchasing Power Parity: The Irish Experience Re-visited," Trinity Economics Papers tep200615, Trinity College Dublin, Department of Economics. [Downloadable!]
Liudas Giraitis & Peter M Robinson, 2002. "Edgeworth Expansions for Semiparametric Whittle Estimation of Long Memory," STICERD - Econometrics Paper Series /2002/438, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]

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