Change Point Detection in the Distribution of the Errors in Dynamic Linear Models

ABSTRACT We develop a new test procedure for detecting changes in the distribution of the errors in (dynamic) linear models. Our framework accommodates misspecification of the dynamic linear model, thereby allowing for the inclusion of lagged dependent variables as regressors and autocorrelated errors. Under the null hypothesis, the distribution of the errors remains the same throughout the sample period, while there are multiple changes in the distribution of the errors under the alternative. Our procedure is based on the cumulative sum (CUSUM) process that compares the empirical distribution functions of the residuals in the first part of the observations and the whole sample. We derive the asymptotic properties of the proposed test statistics. Monte Carlo simulations show that the proposed test has good size control and high power. We provide empirical applications to Phillips curves and capital asset pricing models.