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.
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Notes
- 1.
Weighted Ljung-Box and ARCH-LM statistics of Fisher and Gallagher (2012) are provided by the ugarchfit() function to better account for the distribution of the statistics when applied to residuals from a fitted model; their use and interpretation remains unchanged.
- 2.
These Chi-squared tests are based on the tests of Palm (1996); group indicates the number of bins used in the implementation.
References
Alexander, C. (2001) Market Models: A Guide to Financial Data Analysis, Wiley, Chichester.
Bauwens, L., Laurent, S., and Rombouts, J. V. (2006) Multivariate GARCH models: a survey. Journal of Applied Econometrics, 21(1), 79–109.
Bera, A. K., and Higgins, M. L. (1993) A survey of Arch models. Journal of Economic Surveys, 7, 305–366. [Reprinted in Jarrow (1998).]
Bollerslev, T. (1986) Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 31, 307–327.
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.
Bollerslev, T., Chou, R. Y., and Kroner, K. F. (1992) ARCH modelling in finance. Journal of Econometrics, 52, 5–59. [Reprinted in Jarrow (1998)]
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.
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.
Carroll, R. J., and Ruppert, D. (1988) Transformation and Weighting in Regression, Chapman & Hall, New York.
Duan, J.-C. (1995) The GARCH option pricing model. Mathematical Finance, 5, 13–32. [Reprinted in Jarrow (1998).]
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.
Enders, W. (2004) Applied Econometric Time Series, 2nd ed., Wiley, New York.
Engle, R. F. (1982) Autoregressive conditional heteroskedasticity with estimates of variance of U.K. inflation. Econometrica, 50, 987–1008.
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.
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.
Gourieroux, C. and Jasiak, J. (2001) Financial Econometrics, Princeton University Press, Princeton, NJ.
Hamilton, J. D. (1994) Time Series Analysis, Princeton University Press, Princeton, NJ.
Heston, S. and Nandi, S. (2000) A closed form GARCH option pricing model. The Review of Financial Studies, 13, 585–625.
Hsieh, K. C. and Ritchken, P. (2000) An empirical comparison of GARCH option pricing models. working paper.
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.)
Li, W. K. (2003) Diagnostic checks in time series, CRC Press.
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.
Palm, F.C. (1996) GARCH models of volatility. Handbook of Statistics, 14, 209–240.
Palma, W. and Zevallos, M. (2004). Analysis of the correlation structure of square time series. Journal of Time Series Analysis, 25(4), 529–550.
Pindyck, R. S. and Rubinfeld, D. L. (1998) Econometric Models and Economic Forecasts, Irwin/McGraw Hill, Boston.
Ritchken, P. and Trevor, R. (1999) Pricing options under generalized GARCH and stochastic volatility processes. Journal of Finance, 54, 377–402.
Rossi, P. E. (1996) Modelling Stock Market Volatility, Academic Press, San Diego.
Silvennoinen, A. and Teräsvirta, T (2009) Multivariate GARCH models. In Handbook of Financial Time Series, 201–229, Springer, Berlin.
Tsay, R. S. (2005) Analysis of Financial Time Series, 2nd ed., Wiley, New York.
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.
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Ruppert, D., Matteson, D.S. (2015). GARCH Models. In: Statistics and Data Analysis for Financial Engineering. Springer Texts in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2614-5_14
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