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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
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. 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. 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. 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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  4. 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. Alan Kirman & Gilles Teyssière, 2002. "Microeconomic Models for Long Memory in the Volatility of Financial Time Series," Studies in Nonlinear Dynamics & Econometrics, Berkeley Electronic Press, vol. 5(4), pages 1083-1083. [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. Javier De Peña & Luis A. Gil-Alana, 2003. "Testing of Nonstationary Cycles in Financial Time Series Data," Faculty Working Papers 15/03, School of Economics and Business Administration, University of Navarra. [Downloadable!]
  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!]
  6. Nour Meddahi, 2001. "An Eigenfunction Approach for Volatility Modeling," CIRANO Working Papers 2001s-70, CIRANO. [Downloadable!]
  7. 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 GmbH. [Downloadable!]
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