Parameterizing Unconditional Skewness in Models for Financial Time Series
In this paper we consider the third-moment structure of a class of nonlinear time series models. Empirically it is often found that the marginal distribution of financial time series is skewed. Therefore it is of importance to know what properties a model should possess if it is to accommodate for unconditional skewness. We consider modelling the unconditional mean and variance using models which respond nonlinearly or asymmetrically to shocks. We investigate the implications these models have on the third moment structure of the marginal distribution and different conditions under which the unconditional distribution exhibits skewness as well as nonzero third-order autocovariance structure. With this respect, the asymmetric or nonlinear specification of the conditional mean is found to be of greater importance than the properties of the conditional variance. Several examples are discussed and, whenever possible, explicit analytical expressions are provided for all third order moments and cross-moments. Finally, we introduce a new tool, shock impact curve, that can be used to investigate the impact of shocks on the conditional mean squared error of the return.
|Date of creation:||01 Oct 2005|
|Publication status:||Published as: He, C., Silvennoinen, A. and Teräsvirta, T., 2008, "Parameterizing Unconditional Skewness in Models for Financial Time Series", Journal of Financial Econometrics, 6(2), 208-230.|
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- Kim, Tae-Hwan & White, Halbert, 2004. "On more robust estimation of skewness and kurtosis," Finance Research Letters, Elsevier, vol. 1(1), pages 56-73, March.
- Engle, Robert F & Lilien, David M & Robins, Russell P, 1987. "Estimating Time Varying Risk Premia in the Term Structure: The Arch-M Model," Econometrica, Econometric Society, vol. 55(2), pages 391-407, March.
- Shiqing Ling & Michael McAleer, 2001.
"Stationarity and the Existence of Moments of a Family of GARCH Processes,"
ISER Discussion Paper
0535, Institute of Social and Economic Research, Osaka University.
- Ling, Shiqing & McAleer, Michael, 2002. "Stationarity and the existence of moments of a family of GARCH processes," Journal of Econometrics, Elsevier, vol. 106(1), pages 109-117, January.
- Lawrence R. Glosten & Ravi Jagannathan & David E. Runkle, 1993.
"On the relation between the expected value and the volatility of the nominal excess return on stocks,"
157, Federal Reserve Bank of Minneapolis.
- Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. " On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
- Hansen, Bruce E, 1994.
"Autoregressive Conditional Density Estimation,"
International Economic Review,
Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(3), pages 705-730, August.
- Hansen, B.E., 1992. "Autoregressive Conditional Density Estimation," RCER Working Papers 322, University of Rochester - Center for Economic Research (RCER).
- Tom Doan, "undated". "RATS programs to replicate Hansen's GARCH models with time-varying t-densities," Statistical Software Components RTZ00086, Boston College Department of Economics.
- Markku Lanne & Pentti Saikkonen, 2005.
"Modeling Conditional Skewness in Stock Returns,"
Economics Working Papers
ECO2005/14, European University Institute.
- G. William Schwert, 1988.
"Why Does Stock Market Volatility Change Over Time?,"
NBER Working Papers
2798, National Bureau of Economic Research, Inc.
- Schwert, G William, 1989. " Why Does Stock Market Volatility Change over Time?," Journal of Finance, American Finance Association, vol. 44(5), pages 1115-1153, December.
- Tim Bollerslev, 1986.
"Generalized autoregressive conditional heteroskedasticity,"
EERI Research Paper Series
EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
- Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
- Meddahi, Nour & Renault, Eric, 2004.
"Temporal aggregation of volatility models,"
Journal of Econometrics,
Elsevier, vol. 119(2), pages 355-379, April.
- Nour Meddahi, 2000. "Temporal Aggregation of Volatility Models," Econometric Society World Congress 2000 Contributed Papers 1903, Econometric Society.
- Nour Meddahi & Éric Renault, 2000. "Temporal Aggregation of Volatility Models," CIRANO Working Papers 2000s-22, CIRANO.
- Joseph Chen & Harrison Hong & Jeremy C. Stein, 2000.
"Forecasting Crashes: Trading Volume, Past Returns and Conditional Skewness in Stock Prices,"
NBER Working Papers
7687, National Bureau of Economic Research, Inc.
- Chen, Joseph & Hong, Harrison & Stein, Jeremy C., 2001. "Forecasting crashes: trading volume, past returns, and conditional skewness in stock prices," Journal of Financial Economics, Elsevier, vol. 61(3), pages 345-381, September.
- Hong, Eun Pyo, 1991. "The autocorrelation structure for the GARCH-M process," Economics Letters, Elsevier, vol. 37(2), pages 129-132, October.
- Adrian R. Pagan & G. William Schwert, 1989.
"Alternative Models For Conditional Stock Volatility,"
NBER Working Papers
2955, National Bureau of Economic Research, Inc.
- Pagan, Adrian R. & Schwert, G. William, 1990. "Alternative models for conditional stock volatility," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 267-290.
- Pagan, A.R. & Schwert, G.W., 1989. "Alternative Models For Conditional Stock Volatility," Papers 89-02, Rochester, Business - General.
- Kurt Brannas & Niklas Nordman, 2003.
"An alternative conditional asymmetry specification for stock returns,"
Applied Financial Economics,
Taylor & Francis Journals, vol. 13(7), pages 537-541.
- Brännäs, Kurt & Nordman, Niklas, 2001. "An Alternative Conditional Asymmetry Specification for Stock Returns," Umeå Economic Studies 556, Umeå University, Department of Economics.
- Kurt Brännäs & Niklas Nordman, 2001. "An Alternative Conditional Asymmetry Specification for Stock Returns," CESifo Working Paper Series 448, CESifo Group Munich.
- Harrison Hong & Jeremy C. Stein, 2003. "Differences of Opinion, Short-Sales Constraints, and Market Crashes," Review of Financial Studies, Society for Financial Studies, vol. 16(2), pages 487-525.
- R. F. Engle & A. J. Patton, 2001. "What good is a volatility model?," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 237-245.
- Amado Peiro, 2002. "Skewness in individual stocks at different investment horizons," Quantitative Finance, Taylor & Francis Journals, vol. 2(2), pages 139-146.
- Enrique Sentana, 1995.
"Quadratic ARCH Models,"
Review of Economic Studies,
Oxford University Press, vol. 62(4), pages 639-661.
- Hagerud, Gustaf E., 1997. "Specification Tests for Asymmetric GARCH," SSE/EFI Working Paper Series in Economics and Finance 163, Stockholm School of Economics.
- Engle, Robert F & Ng, Victor K, 1993.
" Measuring and Testing the Impact of News on Volatility,"
Journal of Finance,
American Finance Association, vol. 48(5), pages 1749-1778, December.
- Robert F. Engle & Victor K. Ng, 1991. "Measuring and Testing the Impact of News on Volatility," NBER Working Papers 3681, National Bureau of Economic Research, Inc.
- Eric Jondeau & Michael Rockinger, 2006. "The Impact of News on Higher Moments," Swiss Finance Institute Research Paper Series 06-28, Swiss Finance Institute.
- Richard Harris & C. Coskun Kucukozmen & Fatih Yilmaz, 2004. "Skewness in the conditional distribution of daily equity returns," Applied Financial Economics, Taylor & Francis Journals, vol. 14(3), pages 195-202.
- Hentschel, Ludger, 1995. "All in the family Nesting symmetric and asymmetric GARCH models," Journal of Financial Economics, Elsevier, vol. 39(1), pages 71-104, September.
- C. James Hueng, 2006. "Short-sales constraints and stock return asymmetry: evidence from the Chinese stock markets," Applied Financial Economics, Taylor & Francis Journals, vol. 16(10), pages 707-716.
- González-Rivera Gloria, 1998. "Smooth-Transition GARCH Models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 3(2), pages 1-20, July.
- Harvey, Campbell R. & Siddique, Akhtar, 1999. "Autoregressive Conditional Skewness," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(04), pages 465-487, December.
- Brännäs, Kurt & Nordman, Niklas, 2001.
"Conditional Skewness Modelling for Stock Returns,"
Umeå Economic Studies
562, Umeå University, Department of Economics.
- He, Changli & Ter svirta, Timo, 1999. "FOURTH MOMENT STRUCTURE OF THE GARCH(p,q) PROCESS," Econometric Theory, Cambridge University Press, vol. 15(06), pages 824-846, December.
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