MAXIMUM-LIKELIHOOD-ESTIMATION OF A GARCH-STABLE MODEL

Maximum likelihood is used to estimate a generalized autoregressive co nditional heteroskedastic (GARCH) process where the residuals have a c onditional stable distribution (GARCH-stable). The scale parameter is modelled 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 t he characteristic exponent when the scale parameter follows a GARCH pr ocess. The parameters of the GARCH-stable model are estimated with dai ly 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% significance level in four out of five cases.