Kernel Likelihood Inference for Time Series

. This paper develops non‐parametric techniques for dynamic models whose data have unknown probability distributions. Point estimators are obtained from the maximization of a semiparametric likelihood function built on the kernel density of the disturbances. This approach can also provide Kullback–Leibler cross‐validation estimates of the bandwidth of the kernel densities. Confidence regions are derived from the dual‐empirical likelihood method based on non‐parametric estimates of the scores. Limit theorems for martingale difference sequences support the statistical theory; moreover, simulation experiments and a real case study show the validity of the methods.