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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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  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!]
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  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. Carol Alexander & Elizabeth Sheedy, 2007. "Model-Based Stress Tests: Linking Stress Tests to VaR for Market Risk," ICMA Centre Discussion Papers in Finance icma-dp2007-02, Henley Business School, Reading University. [Downloadable!]
  4. repec:bep:sndecm:11:2007:2:1411-1411 is not listed on IDEAS
  5. Tim Bollerslev, 2008. "Glossary to ARCH (GARCH)," CREATES Research Papers 2008-49, School of Economics and Management, University of Aarhus. [Downloadable!]
  6. 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!]
  7. Mohammed Bouaddi & Jeroen V.K. Rombouts, 2007. "Mixed Exponential Power Asymmetric Conditional Heteroskedasticity," Cahiers de recherche 0749, CIRPEE. [Downloadable!]
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