Normal Mixture GARCH (1,1): Application to Exchange Rate Modelling

Carol Alexandra () and Emese Lazar
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Carol Alexandra: ICMA Centre, University of Reading

ICMA Centre Discussion Papers in Finance from Henley Business School, University of Reading

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 conclusive 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.

Keywords: Volatility regimes; conditional exess kurtosis; normal mixture; heavy trails; exchange rates; conditional hetroscedasticity; GARCH models. (search for similar items in EconPapers)
JEL-codes: C22 C51 C52 (search for similar items in EconPapers)
Pages: 83 pages
Date: 2004-03
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Related works:
Journal Article: Normal mixture GARCH(1,1): applications to exchange rate modelling (2006)
Journal Article: Normal mixture GARCH(1,1): applications to exchange rate modelling (2006)
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