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Autoregressive Conditional Skewness

Published online by Cambridge University Press:  06 April 2009

Campbell R. Harvey
Affiliation:
Duke University, Durham, NC 27708 and National Bureau of Economic Research, Cambridge, MA 02138
Akhtar Siddique
Affiliation:
Georgetown University, Washington, DC 20057.

Abstract

We present a new methodology for estimating time-varying conditional skewness. Our model allows for changing means and variances, uses a maximum likelihood framework with instruments, and assumes a non-central t distribution. We apply this method to daily, weekly, and monthly stock returns, and find that conditional skewness is important. In particular, we show that the evidence of asymmetric variance is consistent with conditional skewness. Inclusion of conditional skewness also impacts the persistence in conditional variance.

Type
Research Article
Copyright
Copyright © School of Business Administration, University of Washington 1999

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References

Bain, L. J.Moments of Noncentral t and Noncentral F Distribution.” American Statistician, 23 (1969), 334.Google Scholar
Bekaert, G., and Harvey, C. R.. “Emerging Equity Market VolatilityJournal of Financial Economics, 43 (01 1997), 2977.CrossRefGoogle Scholar
Bollerslev, T.Generalized Autoregressive Conditional Heteroskedasticity.” Journal of Econometrics, 31 (04 1986), 307327.CrossRefGoogle Scholar
Bollerslev, T.A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of ReturnReview of Economics and Statistics, 69 (08 1987), 542547.CrossRefGoogle Scholar
Bollerslev, T., and Wooldridge, J.. “Quasi-Maximum Likelihood Estimation And Inference in Dynamic Models with Time-Varying Covariances.” Econometric Reviews, 11 (2, 1992), 143172.CrossRefGoogle Scholar
Brennan, M. “Agency and Asset Pricing.” Unpubl. Manuscript, UCLA and London Business School (1993).Google Scholar
Campbell, J. Y.Stock Returns and the Term Structure.” Journal of Financial Economics, 18 (06 1987), 373399.CrossRefGoogle Scholar
Campbell, J. Y., and Hentschel, L.. “No News Is Good News: An Asymmetric Model of Changing Volatility in Stock Returns.” Journal of Financial Economics, 31 (06 1992), 281318.CrossRefGoogle Scholar
Chan, K. C.; Karolyi, G.; and Stulz, R.. “Global Financial Markets and the Risk Premium on U.S. EquityJournal of Financial Economics, 32 (10 1992), 137167.CrossRefGoogle Scholar
Engle, R. F.Autoregressive Conditional Heteroskedasticity with Estimation of the Variance of United Kingdom Inflation.” Econometrica, 50 (07 1982), 9871008.CrossRefGoogle Scholar
Engle, R. F., and Gonzalez-Rivera, G.. “Semiparametric ARCH ModelsJournal of Business and Economic Statistics, 9 (10 1991), 345359.CrossRefGoogle Scholar
Engle, R. F.; Lilien, D. M.; and Robins, R. P.. “Estimating Time Varying Risk Premia in the Term Structure: The Arch-M Model.” Econometrica, 55 (03 1987), 391407.CrossRefGoogle Scholar
Engle, R. F., and Ng, V.. “Measuring and Testing the Impact of News on VolatilityJournal of Finance, 48 (12 1993), 17491778.CrossRefGoogle Scholar
Foster, F. D., and Viswanathan, S.. “Variations in Trading Volume, Return Volatility, and Trading Costs: Evidence on Recent Price Formation Models.” Journal of Finance, 48 (03 1993), 187211.CrossRefGoogle Scholar
French, K.; Schwert, W.; and Stambaugh, R.. “Expected Stock Returns and VolatilityJournal of Financial Economics, 19 (09 1987), 329.CrossRefGoogle Scholar
Glosten, L. R.; Jagannathan, R.; and Runkle, D. E.. “On the Relation between Expected Value and the Volatility of the Nominal Excess Return on StocksJournal of Finance, 48 (12 1993), 17791801.CrossRefGoogle Scholar
Gray, S.Modeling the Conditional Distribution of Interest Rates as a Regime-Switching ProcessJournal of Financial Economics, 42 (09 1996), 2762.CrossRefGoogle Scholar
Hansen, B. E.Autoregressive Conditional Density EstimationInternational Economic Review, 35 (08 1994), 705730.CrossRefGoogle Scholar
Harvey, C. R.Time-Varying Conditional Covariances in Tests of Asset Pricing ModelsJournal of Financial Economics, 24 (10 1989), 289317.CrossRefGoogle Scholar
Harvey, C. R., and Siddique, A.. “Conditional Skewness In Asset Pricing Tests.” Journal of Finance, (forthcoming 1999).Google Scholar
Hentschel, L.All in the Family: Nesting Symmetric and Asymmetric GARCH Models.” Journal of Financial Economics, 39 (1, 1995), 71104.CrossRefGoogle Scholar
Ibbotson Associates. Stocks, Bonds, Bills and Inflation Yearbook. Chicago, IL: Ibbotson Associates (1997).Google Scholar
Kendall, M. G.; Stuart, A.; and Ord, J. K.. Kendall's Advanced Theory of Statistics, Fifth Ed.New York, NY: Oxford Univ. Press (1991).Google Scholar
Lee, S. W., and Hansen, B. E.. “Asymptotic Theory for the GARCH (1,1) Quasi-Maximum Likelihood Estimator.” Econometric Theory, 10 (03 1994), 2952.CrossRefGoogle Scholar
Nelson, D. B.Conditional Heteroskedasticity in Asset Return: A New Approach.” Econometrica, 59 (03 1991), 347370.CrossRefGoogle Scholar
Nelson, D. B.Filtering and Forecasting with Misspecified ARCH Models I: Getting the Right Variance with the Wrong Model.” Journal of Econometrics, 52 (0405 1992), 6190.CrossRefGoogle Scholar
Newey, W.Generalized Method of Moments Specification TestingJournal of Econometrics, 29 (09 1985), 229256.CrossRefGoogle Scholar
Newey, W., and Steigerwald, D.. “Asymptotic Bias for Quasi-Maximum-Likelihood Estimators in Conditional Heteroskedasticity Models.” Econometrica, 65 (05 1997), 587600.CrossRefGoogle Scholar
Pagan, A. R., and Hong, Y. S.. “Nonparametric Estimation and the Risk Premium.” In Nonparametric and Semiparametric Methods in Econometrics and Statistics. Cambridge, England: Cambridge Univ. Press (1991).Google Scholar
Wu, G. “The Determinants of Asymmetric Volatility.” Unpubl. Manuscript, Stanford Univ. (1998).Google Scholar