The empirical likelihood inference is extended to a class of semiparametric models for stationary, weakly dependent series. A partially linear single-index regression is used for the conditional mean of the series given its past, and the present and past values of a vector of covariates. A parametric model for the conditional variance of the series is added to capture further nonlinear effects. We propose a fixed number of suitable moment equations which characterize the mean and variance model. We derive an empirical log-likelihood ratio which includes nonparametric estimators of several functions, and we show that this ratio has the same limit as in the case where these functions are known.

翻译：经验性概率推断扩大到固定、依赖性弱的系列的一组半参数模型。根据过去和当前及过去共同变量矢量的值,该系列的有条件平均值使用部分线性单指数回归值。添加了该系列有条件差异的参数模型以进一步捕捉非线性效应。我们提议了固定数量的适当时数方程式,以作为平均和差异模型的特点。我们得出了一种经验性日志-相似性比率,其中包括若干函数的非参数估测员,我们表明该比率与已知这些函数的情况具有相同的限制。