CONFIDENCE INTERVALS FOR MULTIPLE CHANGE POINTS IN LINEAR MODELS WITH HETEROSCEDASTIC ERRORS

We consider the problem of estimating and deriving confidence intervals for change points in linear models with heteroscedastic errors. A CUSUM process-based estimator is proposed, and we establish its asymptotic properties when the linear regression model exhibits change points in both the regression parameters and the distribution of the errors. This theory motivates the construction of confidence sets for multiple change points by refining preliminary change point estimators and approximating their distribution in a way that is robust to heteroscedasticity. Monte Carlo experiments indicate that the proposed confidence intervals achieve accurate empirical coverage for change-point locations under both homoscedastic and heteroscedastic error structures. In two data applications, we apply the proposed confidence intervals to examine changes in the flattening of the New Keynesian Phillips curve and in cryptocurrency risk factors.