Estimating and Testing Multiple Structural Breaks in Nonparametric Regressions

ABSTRACT We propose a novel approach for estimating and testing multiple structural breaks in nonparametric regressions using the discrete Fourier transform (DFT). By transforming the unknown regression function into the frequency domain via the DFT, we analyze structural breaks within a frequency‐indexed pseudo generalized regression model. This approach circumvents the need for smoothed nonparametric estimation of the regression function. To detect structural breaks, we introduce a generalized sup‐ test, which has power against a class of local alternatives converging at the parametric rate. This test is asymptotically more powerful than existing smoothed nonparametric tests. Furthermore, we develop an information criterion and a sequential testing procedure to determine the appropriate number of breaks. Simulation studies demonstrate the superior finite sample performance of our proposed approach. In an empirical application, we apply our method to investigate the stability of the conditional capital asset pricing model, uncovering significant evidence of structural breaks in both factor loadings and pricing errors.