Bootstrap bandwidth selection in time-varying coefficient models with jumps

The time-varying coefficient models (TVCMs) are very important tools to explore the hidden structure between the time series response variable and its predictors. The assumption that the coefficient functions are smooth can be restrictive in practice. The TVCMs with jumps are needed to be considered. Selection of smoothing parameters plays a critical role in assessing the performance of estimations of coefficient functions. In this article, we first develop a nonparametric two-step estimation procedure for estimating a finite number of jumps of the coefficient functions. Then, based on the estimated jumps, we propose a bootstrapping bandwidth selection procedure in the TVCMs with jumps. Monte Carlo simulations are conducted to evaluate the finite sample performance of the proposed data-driven estimation and bootstrap bandwidth selection procedures. As an illustration, the proposed methodologies are further applied to a real data example.