Estimation of a Time-Varying Parameter with Arbitrary Structural Breaks

Abstract

We consider a linear model with a time-varying parameter and weakly dependent data. No restrictions are placed on the types of time-varying behavior, allowing for arbitrary smooth structural changes and abrupt structural breaks. The time-varying parameter is estimated by a nonlinear orthogonal series estimator with wavelets as the underlying basis. The ability of wavelets to represent parsimoniously spatially inhomogeneous functions yield a minimax estimator which is without spurious jumps in the large sample limit, thereby faithfully capturing the structure breaks in the parameter. We also demonstrate that methods designed only for smooth time-varying parameters break down when applied to our model.