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Pseudo-Maximum Likelihood Estimation of ARCH(8) Models

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Author Info
Peter M Robinson
Paolo Zaffaroni
Abstract

Strong consistency and asymptotic normality of the Gaussian pseudo-maximumlikelihood estimate of the parameters in a wide class of ARCH(8) processesare established. We require the ARCH weights to decay at least hyperbolically,with a faster rate needed for the central limit theorem than for the law of largenumbers. Various rates are illustrated in examples of particular parameteriza-tions in which our conditions are shown to be satisfied.

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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 /2005/495.

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Date of creation: Oct 2005
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Handle: RePEc:cep:stiecm:/2005/495

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Keywords: ARCH(8 )models pseudo-maximum likelihoodestimation asymptotic inference

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  1. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March. [Downloadable!] (restricted)
  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. [Downloadable!] (restricted)
  3. Paolo Zaffaroni, 2003. "Gaussian inference on certain long-range dependent volatility models," Temi di discussione (Economic working papers) 472, Bank of Italy, Economic Research Department. [Downloadable!]
  4. Giraitis, Liudas & Robinson, Peter M., 2001. "Whittle Estimation Of Arch Models," Econometric Theory, Cambridge University Press, vol. 17(03), pages 608-631, July. [Downloadable!]
  5. Ling, Shiqing & McAleer, Michael, 2003. "Asymptotic Theory For A Vector Arma-Garch Model," Econometric Theory, Cambridge University Press, vol. 19(02), pages 280-310, January. [Downloadable!]
  6. Baillie, Richard T. & Bollerslev, Tim & Mikkelsen, Hans Ole, 1996. "Fractionally integrated generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 74(1), pages 3-30, September. [Downloadable!] (restricted)
  7. Giraitis, Liudas & Kokoszka, Piotr & Leipus, Remigijus, 2000. "Stationary Arch Models: Dependence Structure And Central Limit Theorem," Econometric Theory, Cambridge University Press, vol. 16(01), pages 3-22, February. [Downloadable!]
  8. 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)
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  9. Breidt, F. Jay & Crato, Nuno & de Lima, Pedro, 1998. "The detection and estimation of long memory in stochastic volatility," Journal of Econometrics, Elsevier, vol. 83(1-2), pages 325-348. [Downloadable!] (restricted)
  10. Zaffaroni, Paolo & d'Italia, Banca, 2003. "Gaussian inference on certain long-range dependent volatility models," Journal of Econometrics, Elsevier, vol. 115(2), pages 199-258, August. [Downloadable!] (restricted)
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