Functional coefficient time series models with trending regressors

This paper studies a functional coefficient time series model with trending regressors, where the coefficients are unknown functions of time and random variables. We propose a local linear estimation method to estimate the unknown coefficient functions, and establish the corresponding asymptotic theory under mild conditions. We also develop a test procedure to see if the functional coefficients take particular parametric forms. For practical use, we further propose a Bayesian approach to select the bandwidths, and conduct several numerical experiments to examine the finite sample performance of our proposed local linear estimator and the test procedure. The results show that the local linear estimator works well and the proposed test has satisfactory size and power. In addition, our simulation studies show that the Bayesian bandwidth selection method performs better than the cross-validation method. Furthermore, we use the functional coefficient model to study the relationship between consumption per capita and income per capita in United States, and it was shown that the functional coefficient model with our proposed local linear estimator and Bayesian bandwidth selection method performs well in both in-sample fitting and out-of-sample forecasting.