Testing for Breaks Using Alternating Observations

This paper proposes several new tests for structural change in the multivariate linear regression model. One of the most popular alternatives are Sup-Wald type tests along the lines of Bai, Lumsdaine and Stock (1998), which Bernard,Idoudi, Khalaf and Yélou (2007) show to have very large size distortions, especially for high dimensional systems. They propose the use of Monte Carlo type tests to control for size in finite samples. In this paper we propose several procedures that find a balance between the two previous approaches. We first estimate the break point using alternating observations, and then use the estimated breakpoint to create a test statistic either with the whole sample or with the observations not used for the breakpoint estimation. For the latter approach, it is then possible to use Monte Carlo methods to control size. In contrast to the Sup-Wald type tests, which have non-standard asymptotic distributions, we show that our tests are asymptotically distributed Chisquare using methods similar to those in Andrews (2004). Additionally, our tests stay asymptotically valid even when the distributional assumption made for the Monte Carlo adjustments is incorrect. We illustrate the new test statistics in the univariate context of discount rates and changes in the interest rates, and also in the multivariate setting of the Capital Asset Pricing Model.