Maximum Likelihood Estimation of a Garch-Stable Model

Shi-Miin Liu and B Brorsen

Journal of Applied Econometrics, 1995, vol. 10, issue 3, 273-85

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.

Date: 1995
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