Variable Selection Based Testing for Parameter Changes in Regression with Autoregressive Dependence

We consider a regression model with autoregressive terms and propose significance tests for the detection of change points in this model. Our tests are applicable to both low- or moderate dimension and to high-dimension with sparse regressors. The dimension may be high from the practical point of view of economic and business applications, but in our theoretical framework it is fixed. To accommodate practically high dimension, variable selection is incorporated as an integral part of our approach. The regressors and the errors can exhibit general nonlinear dependence and the model incorporates autoregressive dependence. We develop asymptotic justification and evaluate the performance of the tests both on simulated and real economic data. We test for and estimate changes in responses to risk factors of a U.S. energy stocks portfolio and the Industrial Production index. We relate our findings to macroeconomic policy changes and global impact events.