The Mean Variance Mixing GARCH (1,1) model
Here we present a general framework for a GARCH (1,1) type of process with innovations with a probability law of the mean- variance mixing type, therefore we call the process in question the mean variance mixing GARCH \ (1,1) or MVM GARCH\(1,1). One implication is a GARCH\ model with skewed innovations and constant mean dynamics. This is achieved without using a location parameter to compensate for time dependence that affects the mean dynamics. From a probabilistic viewpoint the idea is straightforward. We just construct our stochastic process from the desired behavior of the cumulants. Further we provide explicit expressions for the unconditional second to fourth cumulants for the process in question. In the paper we present a specification of the MVM-GARCH process where the mixing variable is of the inverse Gaussian type. On the basis on this assumption we can formulate a maximum likelihood based approach for estimating the process closely related to the approach used to estimate an ordinary GARCH (1,1). Under the distributional assumption that the mixing random process is an inverse Gaussian i.i.d process the MVM-GARCH process is then estimated on log return data from the Standard and Poor 500 index. An analysis for the conditional skewness and kurtosis implied by the process is also presented in the paper
|Date of creation:||11 Aug 2004|
|Date of revision:|
|Contact details of provider:|| Phone: 1 212 998 3820|
Fax: 1 212 995 4487
Web page: http://www.econometricsociety.org/pastmeetings.asp
More information through EDIRC
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Drost, Feike C & Nijman, Theo E, 1993.
"Temporal Aggregation of GARCH Processes,"
Econometric Society, vol. 61(4), pages 909-27, July.
- Drost, F.C. & Nijman, T.E., 1990. "Temporal aggregation of GARCH processes," Discussion Paper 1990-66, Tilburg University, Center for Economic Research.
- Drost, F.C. & Nijman, T.E., 1992. "Temporal Aggregation of Garch Processes," Papers 9240, Tilburg - Center for Economic Research.
- Drost, F.C. & Nijman, T.E., 1992. "Temporal aggregation of GARCH processes," Discussion Paper 1992-40, Tilburg University, Center for Economic Research.
- Drost, F.C. & Nijman, T.E., 1990. "Temporal Aggregation Of Garch Processes," Papers 9066, Tilburg - Center for Economic Research.
- Drost, Feike C. & Werker, Bas J. M., 1996.
"Closing the GARCH gap: Continuous time GARCH modeling,"
Journal of Econometrics,
Elsevier, vol. 74(1), pages 31-57, September.
- Drost, F.C. & Werker, B.J.M., 1994. "Closing the GARCH gap : Continuous time GARCH modeling," Discussion Paper 1994-2, Tilburg University, Center for Economic Research.
- Lars Forsberg & Tim Bollerslev, 2002. "Bridging the gap between the distribution of realized (ECU) volatility and ARCH modelling (of the Euro): the GARCH-NIG model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 535-548.
- 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.
- Drost, F.C. & Nijman, T.E., 1993. "Temporal aggregation of GARCH processes," Other publications TiSEM 0642fb61-c7f4-4281-b484-4, Tilburg University, School of Economics and Management.
- Hansen, B.E., 1992.
"Autoregressive Conditional Density Estimation,"
RCER Working Papers
322, University of Rochester - Center for Economic Research (RCER).
- 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.
- 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.
- Badrinath, S G & Chatterjee, Sangit, 1988. "On Measuring Skewness and Elongation in Common Stock Return Distributions: The Case of the Market Index," The Journal of Business, University of Chicago Press, vol. 61(4), pages 451-72, October.
- Kraus, Alan & Litzenberger, Robert H, 1976. "Skewness Preference and the Valuation of Risk Assets," Journal of Finance, American Finance Association, vol. 31(4), pages 1085-1100, September.
- Lee, Tom K Y & Tse, Y K, 1991. "Term Structure of Interest Rates in the Singapore Asian Dollar Market," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 6(2), pages 143-52, April-Jun.
- Andersson, Jonas, 2001. "On the Normal Inverse Gaussian Stochastic Volatility Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(1), pages 44-54, January.
- 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.
When requesting a correction, please mention this item's handle: RePEc:ecm:ausm04:323. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Christopher F. Baum)
If references are entirely missing, you can add them using this form.