SEQUENTIAL MONITORING OF CHANGES IN DYNAMIC LINEAR MODELS, APPLIED TO THE U.S. HOUSING MARKET

Abstract

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.