Mixed Normal Conditional Heteroskedasticity
Both unconditional mixed normal distributions and GARCH models with fat-tailed conditional distributions have been employed in the literature for modeling financial data. We consider a mixed normal distribution coupled with a GARCH-type structure (termed MN-GARCH) which allows for conditional variance in each of the components as well as dynamic feedback between the components. Special cases and relationships with previously proposed specifications are discussed and stationarity conditions are derived. For the empirically most relevant GARCH(1,1) case, the conditions for existence of arbitrary integer moments are given and analytic expressions of the unconditional skewness, kurtosis, and autocorrelations of the squared process are derived. Finally, employing daily return data on the NASDAQ index, we provide a detailed empirical analysis and compare both the in-sample fit and out-of-sample forecasting performance of the MN-GARCH as well as recently proposed Markov-switching models. We show that the MN-GARCH approach can generate a plausible disaggregation of the conditional variance process in which the components' volatility dynamics have a clearly distinct behavior, which is, for example, compatible with the well-known leverage effect. Copyright 2004, Oxford University Press.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Volume (Year): 2 (2004)
Issue (Month): 2 ()
|Contact details of provider:|| Postal: Oxford University Press, Great Clarendon Street, Oxford OX2 6DP, UK|
Fax: 01865 267 985
Web page: http://jfec.oxfordjournals.org/
More information through EDIRC
|Order Information:||Web: http://www.oup.co.uk/journals|
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.:
- 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.
- Adrian R. Pagan & G. William Schwert, 1989. "Alternative Models For Conditional Stock Volatility," NBER Working Papers 2955, National Bureau of Economic Research, Inc.
- 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.
- Friend, Irwin & Westerfield, Randolph, 1980. " Co-Skewness and Capital Asset Pricing," Journal of Finance, American Finance Association, vol. 35(4), pages 897-913, September.
- Lin, Bing-Huei & Yeh, Shih-Kuo, 2000. "On the distribution and conditional heteroscedasticity in Taiwan stock prices," Journal of Multinational Financial Management, Elsevier, vol. 10(3-4), pages 367-395, December.
- Vlaar, Peter J G & Palm, Franz C, 1993. "The Message in Weekly Exchange Rates in the European Monetary System: Mean Reversion, Conditional Heteroscedasticity, and Jumps," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(3), pages 351-60, 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.
- Lux, Thomas, 1997. "Time variation of second moments from a noise trader/infection model," Journal of Economic Dynamics and Control, Elsevier, vol. 22(1), pages 1-38, November.
- Kon, Stanley J, 1984. " Models of Stock Returns-A Comparison," Journal of Finance, American Finance Association, vol. 39(1), pages 147-65, March.
- Kai-Li Wang & Christopher Fawson & Christopher B. Barrett & James B. McDonald, 2001.
"A flexible parametric GARCH model with an application to exchange rates,"
Journal of Applied Econometrics,
John Wiley & Sons, Ltd., vol. 16(4), pages 521-536.
- Wang, Kai-Li & Fawson, Christopher B. & Barrett, Christopher B. & McDonald, James B., 1998. "A Flexible Parametric Garch Model With An Application To Exchange Rates," Economics Research Institute, ERI Study Papers 28355, Utah State University, Economics Department.
- 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 705-30, August.
- Hansen, B.E., 1992. "Autoregressive Conditional Density Estimation," RCER Working Papers 322, University of Rochester - Center for Economic Research (RCER).
- Tom Doan, . "RATS programs to replicate Hansen's GARCH models with time-varying t-densities," Statistical Software Components RTZ00086, Boston College Department of Economics.
- Kim, Dongcheol & Kon, Stanley J, 1994. "Alternative Models for the Conditional Heteroscedasticity of Stock Returns," The Journal of Business, University of Chicago Press, vol. 67(4), pages 563-98, October.
- Tucker, Alan L & Pond, Lallon, 1988. "The Probability Distribution of Foreign Exchange Price Changes: Tests of Candidate Processes," The Review of Economics and Statistics, MIT Press, vol. 70(4), pages 638-47, November.
- Kane, Alex, 1982. "Skewness Preference and Portfolio Choice," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 17(01), pages 15-25, March.
- Hamilton, James D., 1988. "Rational-expectations econometric analysis of changes in regime : An investigation of the term structure of interest rates," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 385-423.
- Hamilton, James D. & Susmel, Raul, 1994.
"Autoregressive conditional heteroskedasticity and changes in regime,"
Journal of Econometrics,
Elsevier, vol. 64(1-2), pages 307-333.
- Tom Doan, . "RATS programs to estimate Hamilton-Susmel Markov Switching ARCH model," Statistical Software Components RTZ00083, Boston College Department of Economics.
- Rockinger, Michael & Jondeau, Eric, 2002.
"Entropy densities with an application to autoregressive conditional skewness and kurtosis,"
Journal of Econometrics,
Elsevier, vol. 106(1), pages 119-142, January.
- Rockinger, M. & Jondeau, E., 2001. "Entropy Densities: with an Application to Autoregressive Conditional Skewness and Kurtosis," Working papers 79, Banque de France.
- Mittnik, Stefan & Paolella, Marc S. & Rachev, Svetlozar T., 2000. "Diagnosing and treating the fat tails in financial returns data," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 389-416, November.
- Diebold, Francis X & Gunther, Todd A & Tay, Anthony S, 1998. "Evaluating Density Forecasts with Applications to Financial Risk Management," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 863-83, November.
- Neely, Christopher J., 1999.
"Target zones and conditional volatility: The role of realignments,"
Journal of Empirical Finance,
Elsevier, vol. 6(2), pages 177-192, April.
- Christopher J. Neely, 1998. "Target zones and conditional volatility: the role of realignments," Working Papers 1994-008, Federal Reserve Bank of St. Louis.
- Bowden, Roger J, 1972. "The Generalised Characteristic Equation of a Linear Dynamic System," Econometrica, Econometric Society, vol. 40(1), pages 201-03, 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.
- Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
- Shleifer, Andrei & Summers, Lawrence H, 1990. "The Noise Trader Approach to Finance," Journal of Economic Perspectives, American Economic Association, vol. 4(2), pages 19-33, Spring.
- Peiro, Amado, 1999. "Skewness in financial returns," Journal of Banking & Finance, Elsevier, vol. 23(6), pages 847-862, June.
- Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
- Berkowitz, Jeremy, 2001. "Testing Density Forecasts, with Applications to Risk Management," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(4), pages 465-74, October.
- Vedat Akgiray & G. Geoffrey Booth, 1987. "Compound Distribution Models Of Stock Returns: An Empirical Comparison," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 10(3), pages 269-280, 09.
When requesting a correction, please mention this item's handle: RePEc:oup:jfinec:v:2:y:2004:i:2:p:211-250. 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: (Oxford University Press)or (Christopher F. Baum)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.