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The memory of stochastic volatility models

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  • Robinson, P. M.

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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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 101 (2001)
Issue (Month): 2 (April)
Pages: 195-218

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Handle: RePEc:eee:econom:v:101:y:2001:i:2:p:195-218

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Web page: http://www.elsevier.com/locate/jeconom

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  1. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
  2. Ghysels, E. & Harvey, A. & Renault, E., 1996. "Stochastic Volatility," Cahiers de recherche 9613, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  3. Paolo Zaffaroni & Peter M. Robinson, 1997. "Nonlinear Time Series With Long Memory: A Model for Stochastic Volatility," FMG Discussion Papers dp253, Financial Markets Group.
  4. Ding, Zhuanxin & Granger, Clive W. J., 1996. "Modeling volatility persistence of speculative returns: A new approach," Journal of Econometrics, Elsevier, vol. 73(1), pages 185-215, July.
  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.
  6. Bollerslev, Tim, 1987. "A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return," The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 542-47, August.
  7. 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.
  8. Bollerslev, Tim & Wright, Jonathan H., 2000. "Semiparametric estimation of long-memory volatility dependencies: The role of high-frequency data," Journal of Econometrics, Elsevier, vol. 98(1), pages 81-106, September.
  9. 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.
  10. C. W. J. GRANGER & Zhuanxin DING, 1995. "Some Properties of Absolute Return: An Alternative Measure of Risk," Annales d'Economie et de Statistique, ENSAE, issue 40, pages 67-91.
  11. 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.
  12. Granger, Clive W. J. & Ding, Zhuanxin, 1996. "Varieties of long memory models," Journal of Econometrics, Elsevier, vol. 73(1), pages 61-77, July.
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