On the Identification of Time for Structural Changes by MOSUM-SQ and CUSUM-SQ Procedures

One way to represent a structural change when modeling an economic system is to allow for parameter changes. Besides verifying the existence of such parameter changes, the ultimate purpose of the structural analysis will be to further characterize them. This chapter includes a partial analysis of such a characterization process. Approximate expected values and variances of CUSUM-SQ and MOSUM-SQ statistics are given for various cases of parameter changes, instantaneous as well as gradual. A numerical simulation study of the statistics is also given. The theoretical study and the simulations together demonstrate that identification of time for structural changes is more intricate in the cases of gradual changes, and when the changes occur early during the observed time period.