中文摘要：

本文考虑变系数ARCH—M模型，构造了非参数部分和参数部分的截面似然估计。基于估计的渐近性质，构造了Wald检验统计量来检验模型是否具有条件异方差性。数值模拟结果表明，所构造的估计和Wald统计量具有良好的有限样本性质。

英文摘要：

For the functional coefficient ARCH-M model, estimators for the parametric and nonparametric components are proposed by profile likelihood method. Our estimators are consistency and asymptotic normality. Based on the asymptotic properties, we propose Wald test statistic to test the existence of conditional heteroscedasticity in functional coefficient ARCH-M model. The performance of our method of estimation and test is illustrated by the corresponding simulation.