Statistical inference for single-index-driven varying-coefficient time series model with explanatory variables

Varying-coefficient time series model has gained wide attention because of its flexibility and interpretability. This article considers the single-index-driven varying-coefficient time series model with explanatory variables. It can be seen as a generalization of the autoregressive model with explanatory variables by changing the coefficient of autoregressive part to a single-index structure, or a generalization of the classical linear model by putting a single-index-driven varying-coefficient autoregressive structure into the model. We adopt local linear smoothing and least square methods separately based on an iterative algorithm to estimate unknown link function and parameters. The estimator for the nonparametric part is proved to be asymptotically normal at any fixed point, and the estimators for the parametric part are derived to be asymptotically normal as well. Some simulation studies are carried out to illustrate the model and finite sample performances of the estimators, and a real data example is also conducted.