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Stylized Facts of Financial Time Series and Three Popular Models of Volatility

  • Malmsten, Hans

    ()

    (Dept. of Economic Statistics, Stockholm School of Economics)

  • Teräsvirta, Timo

    ()

    (Dept. of Economic Statistics, Stockholm School of Economics)

Properties of three well-known and frequently applied first-order models for modelling and forecasting volatility in financial series such as stock and exchange rate returns are considered. These are the standard Generalized Autoregressive Conditional Heteroskedasticity (GARCH), the Exponential GARCH and the Autoregressive Stochastic Volatility model. The focus is on finding out how well these models are able to reproduce characteristic features of such series, also called stylized facts. These include high kurtosis and a rather low-starting and slowly decaying autocorrelation function of the squared or absolute-valued observations. Another stylized fact is that the autocorrelations of absolute-valued returns raised to a positive power are maximized when this power equals unity. A number of results for moments of the three models are given as well as the autocorrelation function of squared observations or, when available, the autocorrelation function of the absolute-valued observations raised to a positive power. These results make it possible to consider kurtosis-autocorrelation combinations that can be reproduced with these models and compare them with ones that have been estimated from financial time series. The ability of the models to reproduce the stylized fact that the autocorrelations of powers of absolute-valued observations are maximized when the power equals one is discussed as well. Finally, it is pointed out that none of these basic models can generate realizations with a skewed marginal distribution. Not unexpectedly, a conclusion that emerges from these considerations, largely based on results on the moment structure of these models, is that none of the models dominates the others when it comes to reproducing stylized facts in typical financial time series.

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Paper provided by Stockholm School of Economics in its series SSE/EFI Working Paper Series in Economics and Finance with number 563.

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Length: 42 pages
Date of creation: 25 Aug 2004
Date of revision: 03 Sep 2004
Publication status: Published in European Journal of Pure and Applied Mathematics, 2010, pages 417-443.
Handle: RePEc:hhs:hastef:0563
Contact details of provider: Postal: The Economic Research Institute, Stockholm School of Economics, P.O. Box 6501, 113 83 Stockholm, Sweden
Phone: +46-(0)8-736 90 00
Fax: +46-(0)8-31 01 57
Web page: http://www.hhs.se/
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  1. Lundbergh, Stefan & Teräsvirta, Timo, 1998. "Evaluating GARCH models," SSE/EFI Working Paper Series in Economics and Finance 292, Stockholm School of Economics, revised 03 May 1999.
  2. Ser-Huang Poon & Clive W.J. Granger, 2003. "Forecasting Volatility in Financial Markets: A Review," Journal of Economic Literature, American Economic Association, vol. 41(2), pages 478-539, June.
  3. Rydén, Tobias & Teräsvirta, Timo & Åsbrink, Stefan, 1996. "Stylized Facts of Daily Return Series and the Hidden Markov Model," SSE/EFI Working Paper Series in Economics and Finance 117, Stockholm School of Economics.
  4. 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.
  5. Chen, Yi-Ting & Kuan, Chung-Ming, 2002. "The pseudo-true score encompassing test for non-nested hypotheses," Journal of Econometrics, Elsevier, vol. 106(2), pages 271-295, February.
  6. Roman Liesenfeld & Robert C. Jung, 2000. "Stochastic volatility models: conditional normality versus heavy-tailed distributions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(2), pages 137-160.
  7. Menelaos Karanasos & J. Kim, . "Moments of the ARMA-EGARCH Model," Discussion Papers 00/29, Department of Economics, University of York.
  8. Sentana,E., 1995. "Quadratic Arch Models," Papers 9517, Centro de Estudios Monetarios Y Financieros-.
  9. Malmsten, Hans, 2004. "Evaluating exponential GARCH models," SSE/EFI Working Paper Series in Economics and Finance 564, Stockholm School of Economics, revised 03 Sep 2004.
  10. Lawrence R. Glosten & Ravi Jagannathan & David E. Runkle, 1993. "On the relation between the expected value and the volatility of the nominal excess return on stocks," Staff Report 157, Federal Reserve Bank of Minneapolis.
  11. Eklund, Bruno, 2003. "Estimating confidence regions over bounded domains," SSE/EFI Working Paper Series in Economics and Finance 548, Stockholm School of Economics.
  12. Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford.
  13. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
  14. Sangjoon Kim, Neil Shephard & Siddhartha Chib, . "Stochastic volatility: likelihood inference and comparison with ARCH models," Economics Papers W26, revised version of W, Economics Group, Nuffield College, University of Oxford.
  15. Jan G. De Gooijer & Kurt Brännäs, 2004. "Asymmetries in conditional mean and variance: modelling stock returns by asMA-asQGARCH," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 23(3), pages 155-171.
  16. Nelson, Daniel B & Cao, Charles Q, 1992. "Inequality Constraints in the Univariate GARCH Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(2), pages 229-35, April.
  17. Thomas Mikosch & Cătălin Stărică, 2004. "Nonstationarities in Financial Time Series, the Long-Range Dependence, and the IGARCH Effects," The Review of Economics and Statistics, MIT Press, vol. 86(1), pages 378-390, February.
  18. He, Changli & Teräsvirta, Timo, 1997. "Properties of Moments of a Family of GARCH Processes," SSE/EFI Working Paper Series in Economics and Finance 198, Stockholm School of Economics.
  19. Y.K. Tse & Xibin Zhang & Jun Yu, 2002. "Estimation of Hyperbolic Diffusion Using MCMC Method," Monash Econometrics and Business Statistics Working Papers 18/02, Monash University, Department of Econometrics and Business Statistics.
  20. He, Changli & Ter svirta, Timo & Malmsten, Hans, 2002. "Moment Structure Of A Family Of First-Order Exponential Garch Models," Econometric Theory, Cambridge University Press, vol. 18(04), pages 868-885, August.
  21. Schwert, G William, 1989. " Why Does Stock Market Volatility Change over Time?," Journal of Finance, American Finance Association, vol. 44(5), pages 1115-53, December.
  22. Kim, Tae-Hwan & White, Halbert, 2004. "On more robust estimation of skewness and kurtosis," Finance Research Letters, Elsevier, vol. 1(1), pages 56-73, March.
  23. Jung-Hee Lee & B. Wade Brorsen, 1997. "A non-nested test of GARCH vs. EGARCH models," Applied Economics Letters, Taylor & Francis Journals, vol. 4(12), pages 765-768.
  24. Granger, Clive W. J. & King, Maxwell L. & White, Halbert, 1995. "Comments on testing economic theories and the use of model selection criteria," Journal of Econometrics, Elsevier, vol. 67(1), pages 173-187, May.
  25. Bai, Xuezheng & Russell, Jeffrey R. & Tiao, George C., 2003. "Kurtosis of GARCH and stochastic volatility models with non-normal innovations," Journal of Econometrics, Elsevier, vol. 114(2), pages 349-360, June.
  26. Engle, Robert F & Ng, Victor K, 1993. " Measuring and Testing the Impact of News on Volatility," Journal of Finance, American Finance Association, vol. 48(5), pages 1749-78, December.
  27. He, Changli & Ter svirta, Timo, 1999. "FOURTH MOMENT STRUCTURE OF THE GARCH(p,q) PROCESS," Econometric Theory, Cambridge University Press, vol. 15(06), pages 824-846, December.
  28. 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.
  29. 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.
  30. M. Angeles Carnero, 2004. "Persistence and Kurtosis in GARCH and Stochastic Volatility Models," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(2), pages 319-342.
  31. Andersson, Jonas, 2001. "On the Normal Inverse Gaussian Stochastic Volatility Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(1), pages 44-54, January.
  32. Y. K. Tse & Xibin Zhang & Jun Yu, 2004. "Estimation of hyperbolic diffusion using the Markov chain Monte Carlo method," Quantitative Finance, Taylor & Francis Journals, vol. 4(2), pages 158-169.
  33. Thomas Mikosch & Catalin Starica, 2004. "Non-stationarities in financial time series, the long range dependence and the IGARCH effects," Econometrics 0412005, EconWPA.
  34. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
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