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The Memory of Stochastic Volatility Models

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Author Info
Peter M Robinson

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Abstract

A valid asymptotic expansion for the covariance of functions of multivariate normal vectors is applied to approximate autovariances of time series generated by nonlinear transformation of Gaussian latent variates, and nonlinear functions of these, with special reference to long memory stochastic volatility models, serving to identify the roles played by the underlying Gaussian processes and the nonlinear transformation. Implications for simple stochastic volatility models are examined in detail, with numerical and Monte Carlo calculations, and applications to cyclic behaviour, cross-sectional and temporal aggregation, and multivariate models are discussed.

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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 /2001/410.

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Date of creation: Feb 2001
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Handle: RePEc:cep:stiecm:/2001/410

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Keywords: Stochastic volatility; long memory; nonlinear functions of Gaussian processes;

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References listed on IDEAS
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  1. Granger, Clive W. J. & Ding, Zhuanxin, 1996. "Varieties of long memory models," Journal of Econometrics, Elsevier, vol. 73(1), pages 61-77, July. [Downloadable!] (restricted)
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  2. Ho, Hwai-Chung & Sun, Tze-Chien, 1987. "A central limit theorem for non-instantaneous filters of a stationary Gaussian process," Journal of Multivariate Analysis, Elsevier, vol. 22(1), pages 144-155, June. [Downloadable!] (restricted)
  3. 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.
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  4. 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)
  5. 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)
  6. 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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  7. Zhuanxin Ding & Clive W. J. Granger, 1995. "Some Properties of Absolute Return: An Alternative Measure of Risk," Annales d'Economie et de Statistique, ADRES, issue 40, pages 06, Octobre-D. [Downloadable!]
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  8. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
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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)
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(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.)

  1. F. DePenya & L. Gil-Alana, 2006. "Testing of nonstationary cycles in financial time series data," Review of Quantitative Finance and Accounting, Springer, vol. 27(1), pages 47-65, August. [Downloadable!] (restricted)
    Other versions:
  2. Violetta Dalla & Liudas Giraitis & Javier Hidalgo, 2006. "Consistent estimation of the memory parameterfor nonlinear time series," STICERD - Econometrics Paper Series /2006/497, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
    Other versions:
  3. Bent Jesper Christensen & Morten Ørregaard Nielsen, 2007. "The Effect of Long Memory in Volatility on Stock Market Fluctuations," CREATES Research Papers 2007-03, School of Economics and Management, University of Aarhus. [Downloadable!]
    Other versions:
  4. Peter M Robinson, 2005. "Modelling Memory of Economic and Financial Time Series," STICERD - Econometrics Paper Series /2005/487, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
  5. 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:
  6. Guglielmo Maria Caporale & Luis A. Gil-Alana, 2007. "Long Run and Cyclical Dynamics in the US Stock Market," CESifo Working Paper Series CESifo Working Paper No. , CESifo Group Munich. [Downloadable!]
    Other versions:
  7. Bent Jesper Christensen & Morten Ørregaard Nielsen & Jie Zhu, 2007. "Long Memory in Stock Market Volatility and the Volatility-in-Mean Effect: The FIEGARCH-M Model," CREATES Research Papers 2007-10, School of Economics and Management, University of Aarhus. [Downloadable!]
    Other versions:
  8. Dominique Guegan, 2007. "La persistance dans les marchés financiers," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00179269_v1, HAL. [Downloadable!]
  9. 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!]
  10. Nour Meddahi, 2001. "An Eigenfunction Approach for Volatility Modeling," CIRANO Working Papers 2001s-70, CIRANO. [Downloadable!]
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