In this paper, we consider the empirical likelihood inferences for a class of varying coefficient ARCH-M models, which is an extended version of parametric ARCH-M models. By constructing a weighted auxiliary random vector, we propose a weighted empirical likelihood method for estimating the functional-coefficients. Under some regularity conditions, the constructed empirical log-likelihood ratio is shown to be asymptotically ${\chi }^2$, and then the pointwise confidence interval for functional-coefficient is constructed. Some simulation studies are carried out to compare finite sample performances of the proposed empirical likelihood estimation method with some existing estimation methods under various model settings. A real data analysis is also undertaken to illustrate practical implementation and performance of the proposed estimation procedure.

在本文中，我们考虑了一类可变系数ARCH-M模型的经验似然推断，这是参数化ARCH-M模型的扩展版本。通过构造加权辅助随机向量，我们提出了一种加权经验似然方法来估计功能系数。在某些规律性条件下，构造的经验对数似然比被证明是渐近的${\chi }^{\mathrm{2个}}$，然后构造函数系数的逐点置信区间。进行了一些模拟研究，以比较所提出的经验似然估计方法的有限样本性能与在各种模型设置下现有的一些估计方法的性能。还进行了实际数据分析，以说明所提出的估算程序的实际实施和性能。