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Published online by Cambridge University Press:  23 March 2021

Lajos Horváth
University of Utah
Zhenya Liu*
Renmin University of China and Aix-Marseille University
Shanglin Lu*
Renmin University of China
Address correspondence to Zhenya Liu and Shanglin Lu, School of Finance, Renmin University of China, Beijing100872, China; e-mail:,
Address correspondence to Zhenya Liu and Shanglin Lu, School of Finance, Renmin University of China, Beijing100872, China; e-mail:,


We propose a sequential monitoring scheme to find structural breaks in dynamic linear models. The monitoring scheme is based on a detector and a suitably chosen boundary function. If the detector crosses the boundary function, a structural break is detected. We provide the asymptotics for the procedure under the null hypothesis of stability. The consistency of the procedure is also proved. We derive the asymptotic distribution of the stopping time under the change point alternative. Monte Carlo simulation is used to show the size and the power of our method under several conditions. As an example, we study the real estate markets in Boston and Los Angeles, and at the national U.S. level. We find structural breaks in the markets, and we segment the data into stationary segments. It is observed that the autoregressive parameter is increasing but stays below 1.

© The Author(s), 2021. Published by Cambridge University Press

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Part of the research was done while Shanglin Lu was visiting the University of Utah. We appreciate the support of the Department of Mathematics. We are grateful to three referees for their useful comments. The detailed remarks of Professor Peter C.B. Phillips, Editor in Chief, helped us to provide more general results, remove some unnecessary conditions, and improve the presentation of our results.



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