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

Author

Listed:
  • Carol Alexandra

    () (ICMA Centre, University of Reading)

  • Emese Lazar

    () (ICMA Centre, 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.

Suggested Citation

  • Carol Alexandra & Emese Lazar, 2004. "Normal Mixture GARCH (1,1): Application to Exchange Rate Modelling," ICMA Centre Discussion Papers in Finance icma-dp2004-05, Henley Business School, Reading University.
  • Handle: RePEc:rdg:icmadp:icma-dp2004-05
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    File URL: http://www.icmacentre.ac.uk/pdf/discussion/DP2004-06.pdf
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    More about this item

    Keywords

    Volatility regimes; conditional exess kurtosis; normal mixture; heavy trails; exchange rates; conditional hetroscedasticity; GARCH models.;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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