Likelihood Ratio Type Test and its Critical Values for Structural Change of Unknown Changepoint

This study considers the problem of testing for a structural change of unknown timing in a regression coefficient in the linear regression model. This is a non-standard testing problem and practical important situation facing applied modelers. Simulation methods were used to generate a range of exact critical values of the Likelihood Ratio (LR) type test for different sample sizes, numbers of regressors and types of regressors. We found that the critical values depend on sample size, the number of regressors and to a less extend on the type of explanatory variables. We recommend using the LR type test statistic for testing structural change of unknown timing with our critical value.