Advanced Search
MyIDEAS: Login

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

Contents:

Author Info

  • Malmsten, Hans

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

  • Teräsvirta, Timo

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

Abstract

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.

Download Info

To our knowledge, this item is not available for download. To find whether it is available, there are three options:
1. Check below under "Related research" whether another version of this item is available online.
2. Check on the provider's web page whether it is in fact available.
3. Perform a search for a similarly titled item that would be available.

Bibliographic Info

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

as in new window
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
Email:
Web page: http://www.hhs.se/
More information through EDIRC

Related research

Keywords: Autoregressive conditional heteroskedasticity; evaluation of volatility models; exponential GARCH; GARCH; modelling return series; stochastic volatility;

Find related papers by JEL classification:

This paper has been announced in the following NEP Reports:

References

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.:
as in new window
  1. 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.
  2. Menelaos Karanasos & J. Kim, . "Moments of the ARMA-EGARCH Model," Discussion Papers 00/29, Department of Economics, University of York.
  3. Lundbergh, Stefan & Teräsvirta, Timo, 1998. "Evaluating GARCH models," Working Paper Series in Economics and Finance 292, Stockholm School of Economics, revised 03 May 1999.
  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. 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.
  6. Sangjoon Kim & Neil Shephard, 1994. "Stochastic volatility: likelihood inference and comparison with ARCH models," Economics Papers 3., Economics Group, Nuffield College, University of Oxford.
  7. 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.
  8. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. " On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
  9. 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.
  10. G. William Schwert, 1990. "Why Does Stock Market Volatility Change Over Time?," NBER Working Papers 2798, National Bureau of Economic Research, Inc.
  11. Sentana,E., 1995. "Quadratic Arch Models," Papers 9517, Centro de Estudios Monetarios Y Financieros-.
  12. 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.
  13. 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.
  14. Eklund, Bruno, 2005. "Estimating confidence regions over bounded domains," Computational Statistics & Data Analysis, Elsevier, vol. 49(2), pages 349-360, April.
  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. 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.
  17. 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.
  18. Ghysels, E. & Harvey, A. & Renault, E., 1996. "Stochastic Volatility," Cahiers de recherche 9613, Universite de Montreal, Departement de sciences economiques.
  19. Yi-Ting Chen & Chung-Ming Kuan, 2000. "The Pseudo-True Score Encompassing Test for Non-Nested Hypothesis," Econometric Society World Congress 2000 Contributed Papers 1723, Econometric Society.
  20. 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.
  21. Neil Shephard, 2005. "Stochastic volatility," Economics Series Working Papers 2005-W17, University of Oxford, Department of Economics.
  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. 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.
  24. Thomas Mikosch & Catalin Starica, 2004. "Non-stationarities in financial time series, the long range dependence and the IGARCH effects," Econometrics 0412005, EconWPA.
  25. He, Changli & Terasvirta, Timo, 1999. "Properties of moments of a family of GARCH processes," Journal of Econometrics, Elsevier, vol. 92(1), pages 173-192, September.
  26. 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.
  27. 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.
  28. 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.
  29. Rydén, Tobias & Teräsvirta, Timo & Åsbrink, Stefan, 1996. "Stylized Facts of Daily Return Series and the Hidden Markov Model," Working Paper Series in Economics and Finance 117, Stockholm School of Economics.
  30. 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.
  31. Malmsten, Hans, 2004. "Evaluating exponential GARCH models," Working Paper Series in Economics and Finance 564, Stockholm School of Economics, revised 03 Sep 2004.
  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. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
  34. 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.
Full references (including those not matched with items on IDEAS)

Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as in new window

Cited by:
  1. Manabu Asai & Michael McAleer & Marcelo C. Medeiros, 2011. "Modelling and Forecasting Noisy Realized Volatility," KIER Working Papers 758, Kyoto University, Institute of Economic Research.
  2. McAleer, Michael & Medeiros, Marcelo C., 2008. "A multiple regime smooth transition Heterogeneous Autoregressive model for long memory and asymmetries," Journal of Econometrics, Elsevier, vol. 147(1), pages 104-119, November.
  3. Alberto Mora-Galan & Ana Perez & Esther Ruiz, 2004. "Stochastic Volatility Models And The Taylor Effect," Statistics and Econometrics Working Papers ws046315, Universidad Carlos III, Departamento de Estadística y Econometría.
  4. Matei, Marius, 2011. "Non-Linear Volatility Modeling of Economic and Financial Time Series Using High Frequency Data," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 0(2), pages 116-141, June.
  5. Haas, Markus, 2009. "Persistence in volatility, conditional kurtosis, and the Taylor property in absolute value GARCH processes," Statistics & Probability Letters, Elsevier, vol. 79(15), pages 1674-1683, August.
  6. Teräsvirta, Timo, 2006. "An introduction to univariate GARCH models," Working Paper Series in Economics and Finance 646, Stockholm School of Economics.
  7. Oleg Korenok & Stanislav Radchenko, 2005. "The smooth transition autoregressive target zone model with the Gaussian stochastic volatility and TGARCH error terms with applications," Working Papers 0505, VCU School of Business, Department of Economics.

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:hhs:hastef:0563. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Helena Lundin).

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.