Testing for Structural Change in Time-Varying Nonparametric Regression Models

In this paper, we consider a nonparametric model with a time-varying regression function and locally stationary regressors. We are interested in the question whether the regression function has the same shape over a given time span. To tackle this testing problem, we propose a kernel-based L2-test statistic. We derive the asymptotic distribution of the statistic both under the null and under fixed and local alternatives. To improve the small sample behavior of the test, we set up a wild bootstrap procedure and derive the asymptotic properties thereof. The theoretical analysis of the paper is complemented by a simulation study and a real data example.