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Gaussian inference on certain long-range dependent volatility models

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  • Paolo Zaffaroni

    ()
    (Banca d'Italia)

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    Abstract

    For a class of long memory volatility models, we establish the asymptotic distribution theory of the Gaussian estimator and the Lagrange multiplier test. Both the case of estimation of martingale difference and ARMA levels are considered. A Montecarlo exercise is presented to assess the small sample properties of the Gaussian estimator and the Lagrange multiplier test. An empirical application, using foreign exchange rates and stock index returns, suggests the potential of these models to capture the dynamic features of the data.

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    File URL: http://www.bancaditalia.it/pubblicazioni/econo/temidi/td03/td472_03/td472/tema_472.pdf
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    Bibliographic Info

    Paper provided by Bank of Italy, Economic Research and International Relations Area in its series Temi di discussione (Economic working papers) with number 472.

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    Date of creation: Jun 2003
    Date of revision:
    Handle: RePEc:bdi:wptemi:td_472_03

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    Postal: Via Nazionale, 91 - 00184 Roma
    Web page: http://www.bancaditalia.it
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    Related research

    Keywords: volatility model; nonlinear moving average model; long memory; Whittle estimation; asymptotic distribution theory;

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    References

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    1. 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.
    2. Lo, Andrew W, 1991. "Long-Term Memory in Stock Market Prices," Econometrica, Econometric Society, vol. 59(5), pages 1279-313, September.
    3. 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.
    4. Chamberlain, Gary, 1987. "Asymptotic efficiency in estimation with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 34(3), pages 305-334, March.
    5. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
    6. Hentschel, Ludger, 1995. "All in the family Nesting symmetric and asymmetric GARCH models," Journal of Financial Economics, Elsevier, vol. 39(1), pages 71-104, September.
    7. Gallant, A Ronald & Rossi, Peter E & Tauchen, George, 1993. "Nonlinear Dynamic Structures," Econometrica, Econometric Society, vol. 61(4), pages 871-907, July.
    8. Bollerslev, Tim & Ole Mikkelsen, Hans, 1996. "Modeling and pricing long memory in stock market volatility," Journal of Econometrics, Elsevier, vol. 73(1), pages 151-184, July.
    9. 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.
    10. Peter M Robinson, 2001. "The Memory of Stochastic Volatility Models," STICERD - Econometrics Paper Series /2001/410, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    11. Robinson, P. M., 1978. "Alternative models for stationary stochastic processes," Stochastic Processes and their Applications, Elsevier, vol. 8(2), pages 141-152, December.
    12. Peter M Robinson & Paolo Zaffaroni, 1997. "Modelling Nonlinearity and Long Memory in Time Series - (Now published in 'Nonlinear Dynamics and Time Series', C D Cutler and D T Kaplan (eds), Fields Institute Communications, 11 (1997), pp.61-170.)," STICERD - Econometrics Paper Series /1997/319, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    13. Paolo Zaffaroni, 2000. "Stationarity and Memory of ARCH Models," STICERD - Econometrics Paper Series /2000/383, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    14. Lumsdaine, Robin L, 1996. "Consistency and Asymptotic Normality of the Quasi-maximum Likelihood Estimator in IGARCH(1,1) and Covariance Stationary GARCH(1,1) Models," Econometrica, Econometric Society, vol. 64(3), pages 575-96, May.
    15. 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.
    16. 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.
    17. Weiss, Andrew A., 1986. "Asymptotic Theory for ARCH Models: Estimation and Testing," Econometric Theory, Cambridge University Press, vol. 2(01), pages 107-131, April.
    18. 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.
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    Cited by:
    1. Zaffaroni, Paolo, 2009. "Whittle estimation of EGARCH and other exponential volatility models," Journal of Econometrics, Elsevier, vol. 151(2), pages 190-200, August.
    2. Arteche González, Jesús María & Artiach Escauriaza, Miguel Manuel, 2011. "Doubly fractional models for dynamic heteroskedastic cycles," BILTOKI 2011-03, Universidad del País Vasco - Departamento de Economía Aplicada III (Econometría y Estadística).
    3. Artiach, Miguel, 2012. "Leverage, skewness and amplitude asymmetric cycles," MPRA Paper 41267, University Library of Munich, Germany.
    4. Banerjee, Anindya & Urga, Giovanni, 2005. "Modelling structural breaks, long memory and stock market volatility: an overview," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 1-34.
    5. Peter M. Robinson & Paolo Zafaroni, 2005. "Pseudo-maximum likelihood estimation of ARCH models," LSE Research Online Documents on Economics 4544, London School of Economics and Political Science, LSE Library.
    6. Quan Hoang Vuong, 2004. "Analyses on Gold and US Dollar in Vietnam's Transitional Economy," Working Papers CEB 04-033.RS, ULB -- Universite Libre de Bruxelles.
    7. Peter M Robinson & Paolo Zaffaroni, 2005. "Pseudo-Maximum Likelihood Estimation of ARCH(8) Models," STICERD - Econometrics Paper Series /2005/495, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.

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