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GARCH Models

  • David Ruppert
  • David S. Matteson
Part of the Springer Texts in Statistics book series (STS)

Abstract

As seen in earlier chapters, financial market data often exhibits volatility clustering, where time series show periods of high volatility and periods of low volatility; see, for example, Fig. 14.1. In fact, with economic and financial data, time-varying volatility is more common than constant volatility, and accurate modeling of time-varying volatility is of great importance in financial engineering.

Keywords

Conditional Variance Standardize Residual GARCH Model Exponentially Weighted Move Average Conditional Correlation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Alexander, C. (2001) Market Models: A Guide to Financial Data Analysis, Wiley, Chichester.Google Scholar
  2. Bauwens, L., Laurent, S., and Rombouts, J. V. (2006) Multivariate GARCH models: a survey. Journal of Applied Econometrics, 21(1), 79–109.CrossRefMathSciNetGoogle Scholar
  3. Bera, A. K., and Higgins, M. L. (1993) A survey of Arch models. Journal of Economic Surveys, 7, 305–366. [Reprinted in Jarrow (1998).]Google Scholar
  4. Bollerslev, T. (1986) Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 31, 307–327.CrossRefzbMATHMathSciNetGoogle Scholar
  5. Bollerslev, T. (1990) Modelling the coherence in short-run nominal exchange rates: a multivariate generalized ARCH model. The Review of Economics and Statistics, 72(3), 498–505.CrossRefGoogle Scholar
  6. Bollerslev, T., Chou, R. Y., and Kroner, K. F. (1992) ARCH modelling in finance. Journal of Econometrics, 52, 5–59. [Reprinted in Jarrow (1998)]Google Scholar
  7. Bollerslev, T., Engle, R. F., and Nelson, D. B. (1994) ARCH models, In Handbook of Econometrics, Vol IV, Engle, R.F., and McFadden, D.L., Elsevier, Amsterdam.Google Scholar
  8. Bollerslev, T., Engle, R. F., and Wooldridge, J. M. (1988) A capital asset pricing model with time-varying covariances. Journal of Political Economy, 96, 116–131.CrossRefGoogle Scholar
  9. Carroll, R. J., and Ruppert, D. (1988) Transformation and Weighting in Regression, Chapman & Hall, New York.CrossRefzbMATHGoogle Scholar
  10. Duan, J.-C. (1995) The GARCH option pricing model. Mathematical Finance, 5, 13–32. [Reprinted in Jarrow (1998).]Google Scholar
  11. Duan, J-C., and Simonato, J. G. (2001) American option pricing under GARCH by a Markov chain approximation. Journal of Economic Dynamics and Control, 25, 1689–1718.CrossRefzbMATHMathSciNetGoogle Scholar
  12. Enders, W. (2004) Applied Econometric Time Series, 2nd ed., Wiley, New York.Google Scholar
  13. Engle, R. F. (1982) Autoregressive conditional heteroskedasticity with estimates of variance of U.K. inflation. Econometrica, 50, 987–1008.Google Scholar
  14. Engle, R. F. (2002) Dynamic conditional correlation: A simple class of multivariate generalized autoregressive conditional heteroskedasticity models. Journal of Business & Economic Statistics, 20(3), 339–350.CrossRefMathSciNetGoogle Scholar
  15. Fisher, T.J., and Gallagher, C.M. (2012) New weighted portmanteau statistics for time series goodness of fit testing. Journal of the American Statistical Association, 107(498), 777–787.CrossRefzbMATHMathSciNetGoogle Scholar
  16. Gourieroux, C. and Jasiak, J. (2001) Financial Econometrics, Princeton University Press, Princeton, NJ.zbMATHGoogle Scholar
  17. Hamilton, J. D. (1994) Time Series Analysis, Princeton University Press, Princeton, NJ.zbMATHGoogle Scholar
  18. Heston, S. and Nandi, S. (2000) A closed form GARCH option pricing model. The Review of Financial Studies, 13, 585–625.CrossRefGoogle Scholar
  19. Hsieh, K. C. and Ritchken, P. (2000) An empirical comparison of GARCH option pricing models. working paper.Google Scholar
  20. Jarrow, R. (1998) Volatility: New Estimation Techniques for Pricing Derivatives, Risk Books, London. (This is a collection of articles, many on GARCH models or on stochastic volatility models, which are related to GARCH models.)Google Scholar
  21. Li, W. K. (2003) Diagnostic checks in time series, CRC Press.Google Scholar
  22. Matteson, D. S. and Tsay, R. S. (2011) Dynamic orthogonal components for multivariate time series. Journal of the American Statistical Association, 106(496), 1450–1463.CrossRefzbMATHMathSciNetGoogle Scholar
  23. Palm, F.C. (1996) GARCH models of volatility. Handbook of Statistics, 14, 209–240.CrossRefMathSciNetGoogle Scholar
  24. Palma, W. and Zevallos, M. (2004). Analysis of the correlation structure of square time series. Journal of Time Series Analysis, 25(4), 529–550.CrossRefzbMATHMathSciNetGoogle Scholar
  25. Pindyck, R. S. and Rubinfeld, D. L. (1998) Econometric Models and Economic Forecasts, Irwin/McGraw Hill, Boston.Google Scholar
  26. Ritchken, P. and Trevor, R. (1999) Pricing options under generalized GARCH and stochastic volatility processes. Journal of Finance, 54, 377–402.CrossRefGoogle Scholar
  27. Rossi, P. E. (1996) Modelling Stock Market Volatility, Academic Press, San Diego.Google Scholar
  28. Silvennoinen, A. and Teräsvirta, T (2009) Multivariate GARCH models. In Handbook of Financial Time Series, 201–229, Springer, Berlin.CrossRefGoogle Scholar
  29. Tsay, R. S. (2005) Analysis of Financial Time Series, 2nd ed., Wiley, New York.CrossRefzbMATHGoogle Scholar
  30. Tse, Y. K. and Tsui, A. K. C. (2002) A multivariate generalized autoregressive conditional heteroscedasticity model with time-varying correlations. Journal of Business & Economic Statistics, 20(3), 351–362.CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • David Ruppert
    • 1
  • David S. Matteson
    • 2
  1. 1.Department of Statistical Science and School of ORIECornell UniversityIthacaUSA
  2. 2.Department of Statistical Science Department of Social StatisticsCornell UniversityIthacaUSA

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