Abstract
AbstractMaximum 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 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 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% significance level in four out of five cases.
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