Estimating the locations of multiple change points in the mean

Detecting and estimating the number and locations of multiple change points is difficult. Sometimes a single-change method can locate multiple shifts by recursively dividing the data at the most likely location of a single shift. However, a single-change method may not detect the presence of multiple changes and may not accurately estimate a division point when multiple changes are present. The Schwarz information criterion offers a direct way to estimate the number of shifts, but the locations maximizing the likelihood function must be known for each possible number of shifts. The latter task is computationally infeasible for a realistic amount of data. This paper proposes a general algorithm for estimating the likelihood-maximizing locations and gives an example in which multiple changes are detected. The performance is evaluated using simulation and the proposed method is shown to be superior to the recursive application of a single shift procedure.