IDEAS home Printed from
MyIDEAS: Login to save this paper or follow this series

Modelling Changes in the Unconditional Variance of Long Stock Return Series

  • Cristina Amado


    (Universidade do Minho - NIPE)

  • Timo Terasvirta


    (CREATES, Department of Economics and Business, Aarhus University)

In this paper we develop a testing and modelling procedure for describing the long-term volatility movements over very long return series. For the purpose, we assume that volatility is multiplicatively decomposed into a conditional and an unconditional component as in Amado and Teräsvirta (2011). The latter component is modelled by incorporating smooth changes so that the unconditional variance is allowed to evolve slowly over time. Statistical inference is used for specifying the parameterization of the time-varying component by applying a sequence of Lagrange multiplier tests. The model building procedure is illustrated with an application to daily returns of the Dow Jones Industrial Average stock index covering a period of more than ninety years. The main conclusions are as follows. First, the LM tests strongly reject the assumption of constancy of the unconditional variance. Second, the results show that the long-memory property in volatility may be explained by ignored changes in the unconditional variance of the long series. Finally, based on a formal statistical test we find evidence of the superiority of volatility forecast accuracy of the new model over the GJR-GARCH model at all horizons for a subset of the long return series.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL:
Download Restriction: no

Paper provided by NIPE - Universidade do Minho in its series NIPE Working Papers with number 02/2012.

in new window

Date of creation: 2012
Date of revision:
Handle: RePEc:nip:nipewp:02/2012
Contact details of provider: Postal: Núcleo de Investigação em Políticas Económicas, Escola de Economia e Gestão, Universidade do Minho, P-4710-057 Braga, Portugal
Phone: +351-253604510 ext 5532
Fax: +351-253601380
Web page:

More information through EDIRC

Order Information: Email:

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. 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.
  2. Cristina Amado & Timo Teräsvirta, 2011. "Modelling Volatility by Variance Decomposition," NIPE Working Papers 01/2011, NIPE - Universidade do Minho.
  3. Fiorentini,G. & Calzolari,G. & Panattoni,L., 1995. "Analytic Derivatives and the Computation of Garch Estimates," Papers 9519, Centro de Estudios Monetarios Y Financieros-.
  4. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  5. Amado, Cristina & Teräsvirta, Timo, 2008. "Modelling Conditional and Unconditional Heteroskedasticity with Smoothly Time-Varying Structure," SSE/EFI Working Paper Series in Economics and Finance 691, Stockholm School of Economics.
  6. 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.
  7. Christian T. Brownlees & Giampiero Gallo, 2008. "Comparison of Volatility Measures: a Risk Management Perspective," Econometrics Working Papers Archive wp2008_03, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".
  8. Cătălin Stărică & Clive Granger, 2005. "Nonstationarities in Stock Returns," The Review of Economics and Statistics, MIT Press, vol. 87(3), pages 503-522, August.
  9. Thomas Mikosch & Catalin Starica, 2004. "Non-stationarities in financial time series, the long range dependence and the IGARCH effects," Econometrics 0412005, EconWPA.
  10. Lamoureux, Christopher G & Lastrapes, William D, 1990. "Persistence in Variance, Structural Change, and the GARCH Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(2), pages 225-34, April.
  11. Robert F. Engle & Jose Gonzalo Rangel, 2008. "The Spline-GARCH Model for Low-Frequency Volatility and Its Global Macroeconomic Causes," Review of Financial Studies, Society for Financial Studies, vol. 21(3), pages 1187-1222, May.
  12. Van Bellegem, Sebastien & von Sachs, Rainer, 2004. "Forecasting economic time series with unconditional time-varying variance," International Journal of Forecasting, Elsevier, vol. 20(4), pages 611-627.
  13. Hamilton, James D & Gang, Lin, 1996. "Stock Market Volatility and the Business Cycle," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(5), pages 573-93, Sept.-Oct.
  14. G. William Schwert, 1989. "Business Cycles, Financial Crises, and Stock Volatility," NBER Working Papers 2957, National Bureau of Economic Research, Inc.
  15. Feng, Yuanhua, 2004. "Simultaneously Modeling Conditional Heteroskedasticity And Scale Change," Econometric Theory, Cambridge University Press, vol. 20(03), pages 563-596, June.
  16. Richard T. Baillie & Claudio Morana, 2007. "Modeling Long Memory and Structural Breaks in Conditional Variances: an Adaptive FIGARCH Approach," ICER Working Papers - Applied Mathematics Series 11-2007, ICER - International Centre for Economic Research.
  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. McCracken, Michael W., 2007. "Asymptotics for out of sample tests of Granger causality," Journal of Econometrics, Elsevier, vol. 140(2), pages 719-752, October.
  19. 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.
  20. 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.
  21. Granger, Clive W. J. & Hyung, Namwon, 2004. "Occasional structural breaks and long memory with an application to the S&P 500 absolute stock returns," Journal of Empirical Finance, Elsevier, vol. 11(3), pages 399-421, June.
Full references (including those not matched with items on IDEAS)

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

When requesting a correction, please mention this item's handle: RePEc:nip:nipewp:02/2012. 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: (Maria João Thompson)

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.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.