Wilks’ theorem for semiparametric regressions with weakly dependent data

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