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Normal mixture GARCH(1,1): applications to exchange rate modelling

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Author Info
Emese Lazar (ISMA Centre, University of Reading, Reading RG6 6BA, UK)
Carol Alexander (ISMA Centre, University of Reading, Reading RG6 6BA, UK)

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Abstract

Some recent specifications for GARCH error processes explicitly assume a conditional variance that is generated by a mixture of normal components, albeit with some parameter restrictions. This paper analyses the general normal mixture GARCH(1,1) model which can capture time variation in both conditional skewness and kurtosis. A main focus of the paper is to provide evidence that, for modelling exchange rates, generalized two-component normal mixture GARCH(1,1) models perform better than those with three or more components, and better than symmetric and skewed Student's t-GARCH models. In addition to the extensive empirical results based on simulation and on historical data on three US dollar foreign exchange rates (British pound, euro and Japanese yen), we derive: expressions for the conditional and unconditional moments of all models; parameter conditions to ensure that the second and fourth conditional and unconditional moments are positive and finite; and analytic derivatives for the maximum likelihood estimation of the model parameters and standard errors of the estimates. Copyright © 2006 John Wiley & Sons, Ltd.

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File URL: http://hdl.handle.net/10.1002/jae.849
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Article provided by John Wiley & Sons, Ltd. in its journal Journal of Applied Econometrics.

Volume (Year): 21 (2006)
Issue (Month): 3 ()
Pages: 307-336
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Handle: RePEc:jae:japmet:v:21:y:2006:i:3:p:307-336

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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.:
  1. Baillie, Richard T & Bollerslev, Tim, 1989. "The Message in Daily Exchange Rates: A Conditional-Variance Tale," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(3), pages 297-305, July.
    Other versions:
  2. Epps, Thomas W & Epps, Mary Lee, 1976. "The Stochastic Dependence of Security Price Changes and Transaction Volumes: Implications for the Mixture-of-Distributions Hypothesis," Econometrica, Econometric Society, vol. 44(2), pages 305-21, March. [Downloadable!] (restricted)
  3. L. Bauwens & C.S. Bos & H.K. van Dijk, 1999. "Adaptive Polar Sampling with an application to a Bayes measure of Value-at-Risk," Econometric Institute Report 167, Erasmus University Rotterdam, Econometric Institute. [Downloadable!]
    Other versions:
  4. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold, 2002. "Parametric and Nonparametric Volatility Measurement," NBER Technical Working Papers 0279, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  5. Markus Haas, 2004. "Mixed Normal Conditional Heteroskedasticity," Journal of Financial Econometrics, Oxford University Press, vol. 2(2), pages 211-250. [Downloadable!] (restricted)
  6. Ding, Zhuanxin & Granger, Clive W. J., 1996. "Modeling volatility persistence of speculative returns: A new approach," Journal of Econometrics, Elsevier, vol. 73(1), pages 185-215, July. [Downloadable!] (restricted)
    Other versions:
  7. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38. [Downloadable!] (restricted)
  8. Boothe, Paul & Glassman, Debra, 1987. "The statistical distribution of exchange rates: Empirical evidence and economic implications," Journal of International Economics, Elsevier, vol. 22(3-4), pages 297-319, May. [Downloadable!] (restricted)
  9. Bai, Xuezheng & Russell, Jeffrey R. & Tiao, George C., 2003. "Kurtosis of GARCH and stochastic volatility models with non-normal innovations," Journal of Econometrics, Elsevier, vol. 114(2), pages 349-360, June. [Downloadable!] (restricted)
  10. Huisman, Ronald, et al, 2001. "Tail-Index Estimates in Small Samples," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(2), pages 208-16, April.
  11. 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. [Downloadable!] (restricted)
    Other versions:
  12. Hsieh, David A, 1989. "Testing for Nonlinear Dependence in Daily Foreign Exchange Rates," Journal of Business, University of Chicago Press, vol. 62(3), pages 339-68, July. [Downloadable!] (restricted)
  13. Klaassen, F., 1998. "Improving garch volatility forecasts," Discussion Paper 52, Tilburg University, Center for Economic Research. [Downloadable!]
  14. K. Newey, Whitney, 1985. "Generalized method of moments specification testing," Journal of Econometrics, Elsevier, vol. 29(3), pages 229-256, September. [Downloadable!] (restricted)
  15. Gray, Stephen F., 1996. "Modeling the conditional distribution of interest rates as a regime-switching process," Journal of Financial Economics, Elsevier, vol. 42(1), pages 27-62, September. [Downloadable!] (restricted)
  16. Chris Brooks, 2005. "Autoregressive Conditional Kurtosis," Journal of Financial Econometrics, Oxford University Press, vol. 3(3), pages 399-421. [Downloadable!] (restricted)
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  17. Cai, Jun, 1994. "A Markov Model of Switching-Regime ARCH," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(3), pages 309-16, July.
  18. Hsieh, David A, 1989. "Modeling Heteroscedasticity in Daily Foreign-Exchange Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(3), pages 307-17, July.
  19. V. L. Martin & G. M. Martin & G. C. Lim, 2005. "Parametric pricing of higher order moments in S&P500 options," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(3), pages 377-404. [Downloadable!]
    Other versions:
  20. Baillie, Richard T & Bollerslev, Tim, 1991. "Intra-day and Inter-market Volatility in Foreign Exchange Rates," Review of Economic Studies, Blackwell Publishing, vol. 58(3), pages 565-85, May. [Downloadable!] (restricted)
    Other versions:
  21. Bollerslev, Tim, 1987. "A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return," The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 542-47, August. [Downloadable!] (restricted)
  22. 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. [Downloadable!]
  23. Ole E. Barndorff-Nielsen & Shephard, 2002. "Econometric analysis of realized volatility and its use in estimating stochastic volatility models," Journal Of The Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 253-280. [Downloadable!] (restricted)
    Other versions:
  24. Alexander, Carol, 2004. "Normal mixture diffusion with uncertain volatility: Modelling short- and long-term smile effects," Journal of Banking & Finance, Elsevier, vol. 28(12), pages 2957-2980, December. [Downloadable!] (restricted)
  25. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April. [Downloadable!] (restricted)
  26. Engle, Robert F & Gonzalez-Rivera, Gloria, 1991. "Semiparametric ARCH Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(4), pages 345-59, October.
    Other versions:
  27. Markus Haas, 2004. "A New Approach to Markov-Switching GARCH Models," Journal of Financial Econometrics, Oxford University Press, vol. 2(4), pages 493-530. [Downloadable!] (restricted)
  28. Robert F. Engle & Yin-Feng Gau, 1997. "Conditional Volatility of Exchange Rates Under a Target Zone," University of California at San Diego, Economics Working Paper Series 97-06, Department of Economics, UC San Diego. [Downloadable!]
  29. Bollerslev, Tim & Ghysels, Eric, 1996. "Periodic Autoregressive Conditional Heteroscedasticity," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(2), pages 139-51, April.
    Other versions:
  30. Nelson, Daniel B., 1996. "Asymptotic filtering theory for multivariate ARCH models," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 1-47. [Downloadable!] (restricted)
  31. Robert Engle & Tim Bollerslev, 1986. "Modelling the persistence of conditional variances," Econometric Reviews, Taylor and Francis Journals, vol. 5(1), pages 1-50. [Downloadable!] (restricted)
  32. Fernandez, C. & Steel, M.F.J., 1996. "On Bayesian modelling of fat tails and skewness," Discussion Paper 58, Tilburg University, Center for Economic Research. [Downloadable!]
  33. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July. [Downloadable!] (restricted)
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Cited by:
(explanations, 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.)

  1. Markus Haas & Stefan Mittnik & Bruce Mizrach, 2004. "Assessing Central Bank Credibility During the EMS Crises: Comparing Option and Spot Market-Based Forecasts," Departmental Working Papers 200424, Rutgers University, Department of Economics. [Downloadable!]
    Other versions:
  2. Markus Haas & Stefan Mittnik & Marc S. Paolella, 2006. "Multivariate Normal Mixture GARCH," CFS Working Paper Series 2006/09, Center for Financial Studies. [Downloadable!]
  3. Markus Haas, 2007. "Volatility Components and Long Memory-Effects Revisited," Studies in Nonlinear Dynamics & Econometrics, Berkeley Electronic Press, vol. 11(2), pages 1411-1411. [Downloadable!] (restricted)
  4. Christoph Hartz & Stefan Mittnik & Marc S. Paolella, 2006. "Accurate Value-at-Risk Forecast with the (good old) Normal-GARCH Model," CFS Working Paper Series 2006/23, Center for Financial Studies. [Downloadable!]
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