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Maximum Likelihood Estimation of a Garch-Stable Model

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  • Liu, Shi-Miin
  • Brorsen, B Wade

Abstract

Maximum likelihood is used to estimate a generalized autoregressive conditional heteroskedastic (GARCH) process where the residuals have a conditional stable distribution (GARCH-stable). The scale parameter is modeled such that a GARCH process with normally distributed residuals is a special case. The usual methods of estimating the parameters of the stable distribution assume constant scale and will underestimate the characteristic exponent when the scale parameter follows a GARCH process. The parameters of the GARCH-stable model are estimated with daily foreign currency returns. Estimates of characteristic exponents are higher with the GARCH-stable than when independence is assumed. Monte Carlo hypothesis testing procedures, however, reject our GARCH-stable model at the 1 percent significance level in four out of five cases. Copyright 1995 by John Wiley & Sons, Ltd.

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  • Liu, Shi-Miin & Brorsen, B Wade, 1995. "Maximum Likelihood Estimation of a Garch-Stable Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 10(3), pages 273-285, July-Sept.
  • Handle: RePEc:jae:japmet:v:10:y:1995:i:3:p:273-85
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