Testing for structural change in AR(1) models with wavelets

This paper develops a new procedure to test the changes in the autocorrelation structure of an AR(1) process by constructing a test statistic of cumulative sum (CUSUM) of squares based on a specific frequency decomposition of the variance using the maximal overlap discrete wavelet transformation (MODWT). The wavelet approach is appealing since it is based directly on the different behavior of the spectra of autoregressive processes with different coefficients. A feasible version of the test and the empirical quantiles of the test statistic are given. We demonstrate the size and power properties of the proposed test through Monte Carlo simulations.