Maximum likelihood estimation of a GARCH‐stable model
用最大似然法估计残差服从稳定分布的GARCH模型，发现用外汇日收益率数据估计的特征指数比假设独立时更高，但蒙特卡洛检验在5个案例中4个在1%水平上拒绝了该模型。
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 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.