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The empirical likelihood inference is extended to a class of semiparametricmodels for stationary, weakly dependent series. A partially linear single-indexregression is used for the conditional mean of the series given its past, andthe present and past values of a vector of covariates. A parametric model forthe conditional variance of the series is added to capture further nonlineareffects. We propose a fixed number of suitable moment equations whichcharacterize the mean and variance model. We derive an empirical log-likelihoodratio which includes nonparametric estimators of several functions, and we showthat this ratio has the same limit as in the case where these functions areknown.

Wilks' theorem for semiparametric regressions with weakly dependent data