Jump-detection-based estimation in time-varying coefficient models and empirical applications

Time-varying coefficient models are very important tools to explore the hidden structure between the response variable and its predictors. In some applications, the coefficient curves have singularities, including jump points at some unknown positions, representing structural changes of the related processes. Detection of such singularities is important for understanding the structural changes. In this paper, an alternative jump-detection procedure is proposed based on the first-order and second-order derivatives of the coefficient curves. Based on the detected jump points, a coefficient curve estimation procedure is also proposed, which can preserve the jump structure well when the noise level is small. Further, the implementation of turning parameters is discussed. Under some mild conditions, the asymptotic properties of the proposed estimators are established not only in the continuous regions of coefficient functions, but also in the neighborhoods of the jump points. Finally, we demonstrate, using both simulation and empirical examples, that the proposed methodologies perform well.