Functional index coefficient models with variable selection

We consider model (variable) selection in a semi-parametric time series model with functional coefficients. Variable selection in the semi-parametric model must account for the fact that the parametric part of the model is estimated at a faster convergence rate than the nonparametric component. Our variable selection procedures employ a smoothly clipped absolute deviation penalty function and consist of two steps. The first is to select covariates with functional coefficients that enter in the semi-parametric model. Then, we perform variable selection for variables with parametric coefficients. The asymptotic properties, such as consistency, sparsity and the oracle property of these two-step estimators are established. A Monte Carlo simulation study is conducted to examine the finite sample performance of the proposed estimators and variable selection procedures. Finally, an empirical example exploring the predictability of asset returns demonstrates the practical application of the proposed functional index coefficient autoregressive models and variable selection procedures.