Testing serial correlation for partially nonlinear models

Partially nonlinear models, as extensions of partially linear models are extensively used in statistical modeling. This paper considers the spline empirical log-likelihood ratio for testing serial correlation in partially nonlinear models. It is shown that the proposed empirical log-likelihood ratio converges to the standard chi-square distribution under the null hypothesis of no serial correlation. Some simulations are conducted to estimate the rejection probabilities under the null hypothesis and serial correlation. An example of application is also illustrated.