Advanced Search
MyIDEAS: Login to save this paper or follow this series

Modeling and Forecasting the Volatility of the Nikkei 225 Realized Volatility Using the ARFIMA-GARCH Model

Contents:

Author Info

  • Isao Ishida

    (Faculty of Economics and Graduate School of Public Policy, University of Tokyo)

  • Toshiaki Watanabe

    (Institute of Economic Research, Hitotsubashi University)

Abstract

In this paper, we apply the ARFIMA-GARCH model to the realized volatility and the continuous sample path variations constructed from high-frequency Nikkei 225 data. While the homoskedastic ARFIMA model performs excellently in predicting the Nikkei 225 realized volatility time series and their square-root and log transformations, the residuals of the model suggest presence of strong conditional heteroskedasticity similar to the finding of Corsi et al. (2007) for the realized S&P 500 futures volatility. An ARFIMA model augmented by a GARCH(1,1) specification for the error term largely captures this and substantially improves the fit to the data. In a multi-day forecasting setting, we also find some evidence of predictable time variation in the volatility of the Nikkei 225 volatility captured by the ARFIMA-GARCH model.

Download Info

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: http://www.cirje.e.u-tokyo.ac.jp/research/dp/2009/2009cf608.pdf
Download Restriction: no

Bibliographic Info

Paper provided by CIRJE, Faculty of Economics, University of Tokyo in its series CIRJE F-Series with number CIRJE-F-608.

as in new window
Length: 32pages
Date of creation: Jan 2009
Date of revision:
Handle: RePEc:tky:fseres:2009cf608

Contact details of provider:
Postal: Hongo 7-3-1, Bunkyo-ku, Tokyo 113-0033
Phone: +81-3-5841-5644
Fax: +81-3-5841-8294
Email:
Web page: http://www.cirje.e.u-tokyo.ac.jp/index.html
More information through EDIRC

Related research

Keywords:

Other versions of this item:

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. Ole Barndorff-Nielsen & Svend Erik Graversen & Jean Jacod & Mark Podolskij & Neil Shephard, 2004. "A Central Limit Theorem for Realised Power and Bipower Variations of Continuous Semimartingales," Economics Papers 2004-W29, Economics Group, Nuffield College, University of Oxford.
  2. Diebold, Francis X & Gunther, Todd A & Tay, Anthony S, 1998. "Evaluating Density Forecasts with Applications to Financial Risk Management," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 863-83, November.
  3. 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.
  4. Ole E. Barndorff-Nielsen & Neil Shephard, 2000. "Econometric analysis of realised volatility and its use in estimating stochastic volatility models," Economics Papers 2001-W4, Economics Group, Nuffield College, University of Oxford, revised 05 Jul 2001.
  5. Robinson, P.M. & Henry, M., 1999. "Long And Short Memory Conditional Heteroskedasticity In Estimating The Memory Parameter Of Levels," Econometric Theory, Cambridge University Press, vol. 15(03), pages 299-336, June.
  6. Ole E. Barndorff-Nielsen & Neil Shephard, 2004. "Econometrics of testing for jumps in financial economics using bipower variation ," OFRC Working Papers Series 2004fe01, Oxford Financial Research Centre.
  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. Corsi, Fulvio & Kretschmer, Uta & Mittnik, Stefan & Pigorsch, Christian, 2005. "The volatility of realized volatility," CFS Working Paper Series 2005/33, Center for Financial Studies (CFS).
  9. Peter M. Robinson & M. Henry, 1999. "Long and short memory conditional heteroskedasticity in estimating the memory parameter of levels," LSE Research Online Documents on Economics 304, London School of Economics and Political Science, LSE Library.
  10. Koopman, Siem Jan & Jungbacker, Borus & Hol, Eugenie, 2005. "Forecasting daily variability of the S&P 100 stock index using historical, realised and implied volatility measurements," Journal of Empirical Finance, Elsevier, vol. 12(3), pages 445-475, June.
  11. Deo, Rohit S. & Hurvich, Clifford M., 2001. "On The Log Periodogram Regression Estimator Of The Memory Parameter In Long Memory Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 17(04), pages 686-710, August.
  12. Chen, Yi-Ting & Chou, Ray Y. & Kuan, Chung-Ming, 2000. "Testing time reversibility without moment restrictions," Journal of Econometrics, Elsevier, vol. 95(1), pages 199-218, March.
  13. Guglielmo Maria Caporale & Christos Ntantamis & Theologos Pantelidis & Nikitas Pittis, 2004. "The Bds Test As A Test For The Adequacy Of A Garch(1,1) Specification: A Monte Carlo Study," Public Policy Discussion Papers 04-14, Economics and Finance Section, School of Social Sciences, Brunel University.
  14. Baillie, Richard T & Chung, Ching-Fan & Tieslau, Margie A, 1996. "Analysing Inflation by the Fractionally Integrated ARFIMA-GARCH Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(1), pages 23-40, Jan.-Feb..
  15. Yi-Ting Chen & Chung-Ming Kuan, 2002. "Time irreversibility and EGARCH effects in US stock index returns," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 565-578.
  16. Ole E. Barndorff-Nielsen, 2004. "Power and Bipower Variation with Stochastic Volatility and Jumps," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(1), pages 1-37.
  17. Pascal Bondon & Wilfredo Palma, 2007. "A Class of Antipersistent Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(2), pages 261-273, 03.
  18. Francis X. Diebold & James M. Nason, 1989. "Nonparametric exchange rate prediction?," Finance and Economics Discussion Series 81, Board of Governors of the Federal Reserve System (U.S.).
  19. Andersen, Torben G & Bollerslev, Tim, 1998. "Answering the Skeptics: Yes, Standard Volatility Models Do Provide Accurate Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 885-905, November.
  20. Andersen, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Ebens, Heiko, 2001. "The distribution of realized stock return volatility," Journal of Financial Economics, Elsevier, vol. 61(1), pages 43-76, July.
  21. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
  22. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2001. "Modeling and Forecasting Realized Volatility," NBER Working Papers 8160, National Bureau of Economic Research, Inc.
  23. Andersen, Torben G. & Bollerslev, Tim & Cai, Jun, 2000. "Intraday and interday volatility in the Japanese stock market," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 10(2), pages 107-130, June.
  24. Hansen, Peter Reinhard & Lunde, Asger, 2006. "Consistent ranking of volatility models," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 97-121.
  25. 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.
  26. Jensen, S ren Tolver & Rahbek, Anders, 2004. "Asymptotic Inference For Nonstationary Garch," Econometric Theory, Cambridge University Press, vol. 20(06), pages 1203-1226, December.
  27. Bollerslev, Tim & Ole Mikkelsen, Hans, 1996. "Modeling and pricing long memory in stock market volatility," Journal of Econometrics, Elsevier, vol. 73(1), pages 151-184, July.
  28. Andersen T. G & Bollerslev T. & Diebold F. X & Labys P., 2001. "The Distribution of Realized Exchange Rate Volatility," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 42-55, March.
  29. Andersen, Torben G. & Bollerslev, Tim & Lange, Steve, 1999. "Forecasting financial market volatility: Sample frequency vis-a-vis forecast horizon," Journal of Empirical Finance, Elsevier, vol. 6(5), pages 457-477, December.
  30. Egorov, Alexei V. & Hong, Yongmiao & Li, Haitao, 2006. "Validating forecasts of the joint probability density of bond yields: Can affine models beat random walk?," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 255-284.
  31. Whitney K. Newey & Douglas G. Steigerwald, 1997. "Asymptotic Bias for Quasi-Maximum-Likelihood Estimators in Conditional Heteroskedasticity Models," Econometrica, Econometric Society, vol. 65(3), pages 587-600, May.
  32. Thomakos, Dimitrios D. & Wang, Tao, 2003. "Realized volatility in the futures markets," Journal of Empirical Finance, Elsevier, vol. 10(3), pages 321-353, May.
  33. Yongmiao Hong, 2005. "Nonparametric Specification Testing for Continuous-Time Models with Applications to Term Structure of Interest Rates," Review of Financial Studies, Society for Financial Studies, vol. 18(1), pages 37-84.
  34. Sowell, Fallaw, 1992. "Maximum likelihood estimation of stationary univariate fractionally integrated time series models," Journal of Econometrics, Elsevier, vol. 53(1-3), pages 165-188.
  35. Siem Jan Koopman & Marius Ooms & M. Angeles Carnero, 2005. "Periodic Seasonal Reg-ARFIMA-GARCH Models for Daily Electricity Spot Prices," Tinbergen Institute Discussion Papers 05-091/4, Tinbergen Institute.
  36. Velasco, Carlos, 1999. "Non-stationary log-periodogram regression," Journal of Econometrics, Elsevier, vol. 91(2), pages 325-371, August.
  37. Neil Shephard & Ole E. Barndorff-Nielsen, 2003. "Power and bipower variation with stochastic volatility and jumps," Economics Series Working Papers 2003-W18, University of Oxford, Department of Economics.
  38. Lee, Sang-Won & Hansen, Bruce E., 1994. "Asymptotic Theory for the Garch(1,1) Quasi-Maximum Likelihood Estimator," Econometric Theory, Cambridge University Press, vol. 10(01), pages 29-52, March.
  39. Guglielmo Maria Caporale, 2005. "The BDS Test as a Test for the Adequacy of a GARCH(1,1) Specification: A Monte Carlo Study," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 3(2), pages 282-309.
  40. Martens, Martin, 2001. "Forecasting daily exchange rate volatility using intraday returns," Journal of International Money and Finance, Elsevier, vol. 20(1), pages 1-23, February.
  41. 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.
Full references (including those not matched with items on IDEAS)

Citations

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:tky:fseres:2009cf608. 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: (CIRJE administrative office).

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.