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This paper studies the least squares estimation of a change point in multiple regressions. Consistency, rate of convergence, and asymptotic distributions are obtained. The model allows for lagged dependent variables and trending regressors. The error process can be dependent and heteroskedastic. For nonstationary regressors or disturbances, the asymptotic distribution is shown to be skewed. The analytical density function and the cumulative distribution function for the general skewed distribution are derived. The analysis applies to both pure and partial changes. The method is used to analyze the response of market interest rates to discount rate changes.
Jushan Bai (Sat,) studied this question.