Semiparametric ARCH Models
提出一种半参数ARCH模型，用参数形式刻画条件均值和方差，用非参数方法估计条件密度，并通过蒙特卡洛实验和实际数据（小公司股票日收益率、英镑兑美元汇率）展示其效率优势。
This article introduces a semiparametric autoregressive conditional heteroscedasticity (ARCH) model that has conditional first and second moments given by autoregressive moving average and ARCH parametric formulations but a conditional density that is assumed only to be sufficiently smooth to be approximated by a nonparametric density estimator. For several particular conditional densities, the relative efficiency of the quasi-maximum likelihood estimator is compared with maximum likelihood under correct specification. These potential efficiency gains for a fully adaptive procedure are compared in a Monte Carlo experiment with the observed gains from using the proposed semiparametric procedure, and it is found that the estimator captures a substantial proportion of the potential. The estimator is applied to daily stock returns from small firms that are found to exhibit conditional skewness and kurtosis and to the British pound to dollar exchange rate.