Stopping Tests in the Sequential Estimation for Multiple Structural Breaks

In this paper, we propose the use of bootstrapping methods to obtain correct critical values for dating breaks. Following the procedure proposed in Banerjee, Lazarova and Urga (1998), we consider the case of estimating a system with two or more marginal processes and a conditional process. First, the location of the breaks in marginal models is estimated. Next, the marginal models are imposed on the conditional model to form a reduced form system. The conditional model with its own breaks is then estimated. The estimation of the break dates is sequential. Break dates are estimated via two alternative procedures: including estimated break dates one by one or splitting the sample. Inclusion of additional breaks or splitting samples are repeated until a criterion for stopping is satisfied. In this paper we propose bootstrap tests as criterion for stopping sequential search. This procedure allows to improve the estimators to avoid excessive bias and prove to be stable in the case of both stationary and non-stationary series. Finally, we illustrate the methods by modelling the money demand in United Kingdom