A New Class of Change Point Test Statistics of Rényi Type

A new class of change point test statistics is proposed that utilizes a weighting and trimming scheme for the cumulative sum (CUSUM) process inspired by Rényi. A thorough asymptotic analysis and simulations both demonstrate that this new class of statistics possess superior power compared to traditional change point statistics based on the CUSUM process when the change point is near the beginning or end of the sample. Generalizations of these “Rényi” statistics are also developed to test for changes in the parameters in linear and nonlinear regression models, and in generalized method of moments estimation. In these contexts, we applied the proposed statistics, as well as several others, to test for changes in the coefficients of Fama–French factor models. We observed that the Rényi statistic was the most effective in terms of retrospectively detecting change points that occur near the endpoints of the sample.