Strong rules for detecting the number of breaks in a time series

This paper proposes a new approach for detecting the number of structural breaks in a time series when estimation of the breaks is performed one at the time. We consider the case of shifts in the mean of a possibly nonlinear process, allowing for dependent and heterogeneous observations. This is accomplished through a simple, sequential, almost sure rule ensuring that, in large samples, both the probabilities of overestimating and underestimating the number of breaks are zero. A new estimator for the long run variance which is consistent also in the presence of neglected breaks is proposed. The finite sample behavior is investigated via a simulation exercise. A tendency to overreject the null hypothesis emerges for sample of moderate size, and so we suggest a small sample correction. The sequential procedure, applied to the weekly Eurodollar interest rate, detects multiple breaks over the period 1973–1995.