Abstract
Previous chapters have concentrated on modeling and predicting the conditional mean, or the first order moment, of a univariate time series, and are rarely concerned with the conditional variance, or the second order moment, of a time series. However, it is well known that in financial markets large changes tend to be followed by large changes, and small changes tend to be followed by small changes. In other words, the financial markets are sometimes more volatile, and sometimes less active.
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7.10 References
Alexander, C. (2001). Market Models: A Guide to Financial Data Analysis, John Wiley & Sons, Chichester, UK.
Bera, A.K. and M.L. Higgins (1995). “On ARCH Models: Properties, Estimation and Testing,” Journal of Economic Surveys, 7, 305–362.
Black, F. (1976). “Studies in Stock Price Volatility Changes,” Proceedings of the 1976 Business Meeting of the Business and Economics Statistics Section, American Statistical Association, 177–181.
Bollerslev, T. (1986). “Generalized Autoregressive Conditional Heteroskedasticity,” Journal of Econometrics, 31, 307–327.
Bollerslev, T., R.Y. Chu and K.F. Kroner (1994). “ARCH Modeling in Finance: A Selective Review of the Theory and Empirical Evidence,” Journal of Econometrics, 52, 5–59.
Bollerslev, T., Engle, R. F., and Nelson, D. B. (1994). “ARCH Models,” in R. F. Engle and D. L. McFadden (eds.), Handbook of Econometrics, Vol. 4, Elsevier Science B. V., Amsterdam.
Bollerslev, T., and Wooldrige, J. M. (1992). “Quasi-maximum Likelihood Estimation and Inference in Dynamic Models with Time-varying Covariances,” Econometric Reviews, 11, 143–172.
Davidson, R., MacKinnon, J. G. (1993). Estimation and Inference in Econometrics, Oxford University Press, Oxford.
Diebold, F.X. and J.A. Lopez (1996). “Modeling Volatility Dynamics,” in K. Hoover (ed.) Macroeconomics: Developments, Tensions and Prospects. Kluwer, Boston.
Ding, Z., and Granger, C. W. J. (1996). “Modeling Volatility Persistence of Speculative Returns: A New Approach,” Journal of Econometrics, 73, 185–215.
Ding, Z., Granger, C. W. J., and Engle, R. F. (1993). “A Long Memory Property of Stock Market Returns and a New Model,” Journal of Empirical Finance, 1, 83–106.
Engle, R. F. (1982). “Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of United Kingdom Inflation,” Econometrica, 50(4), 987–1007.
Engle, R. F., and Lee, G. J. (1999). “A Long-Run and Short-Run Component Model of Stock Return Volatility,” in R. F. Engle and H. White (eds.), Cointegration, Causality, and Forecasting. Oxford University Press, Oxford.
Engle, R. F., Lilien, D. M., and Robins, R. P. (1987). “Estimating Time Varying Risk Premia in the Term-Structure: the ARCH-M Model,” Econometrica, 55(2), 391–407.
Engle, R. F., and Ng, V. (1993). “Measuring and Testing the Impact of News on Volatility,” Journal of Finance, 48(5), 1749–1778.
Engle, R.F. (2001). “GARCH 101: The Use of ARCH/GARCH Models in Applied Economics,” Journal of Economic Perspectives, 15, 157–168.
Engle, R.F. and A.J. Patton (2001). “What Good is a Volatility Model?” QuantitativeFinance, 237–245.
Glosten, L. R., Jagannathan, R., and Runkle, D. E. (1993). “On the Relation Between the Expected Value and the Volatility of the Nominal Excess Return on Stocks,” Journal of Finance, 48(5), 1779–1801.
Hamilton, J. D. (1994). Time Series Analysis. Princeton University Press, Princeton, NJ.
He, C., Teräsvirta, T. (1999a). “Properties of Moments of a Family of GARCH Processes,” Journal of Econometrics, 92, 173–192.
He, C., Teräsvirta, T. (1999b). “Fourth Moment Structure of the GARCH(p, q) Process,” Econometric Theory, 15, 824–846.
Nelson, D. B. (1991). “Conditional Heteroskedasticity in Asset Returns: a New Approach,” Econometrica, 59(2), 347–370.
Nelson, D. B., and Cao, C. Q. (1992). “Inequality Constraints in the Univariate GARCH Model,” Journal of Business and Economic Statistics, 10(2), 229–235.
Tsay, R.S. (2001). Analysis of Financial Time Series, John Wiley & Sons, New York.
Zakoian, M. (1994), “Threshold Heteroscedastic Models,” Journal of Economic Dynamics and Control, 18, 931–955.
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(2006). Univariate GARCH Modeling. In: Modeling Financial Time Series with S-PLUS®. Springer, New York, NY. https://doi.org/10.1007/978-0-387-32348-0_7
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DOI: https://doi.org/10.1007/978-0-387-32348-0_7
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