Testing for Breaks Using Alternating Observations

This paper proposes several new tests for structural change in themultivariate 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, especiallyfor high dimensional systems. They propose the use of Monte Carlo type tests tocontrol for size in finite samples. In this paper we propose several procedures thatfind a balance between the two previous approaches. We first estimate the breakpoint using alternating observations, and then use the estimated breakpoint to createa test statistic either with the whole sample or with the observations not used forthe breakpoint estimation. We show that these tests are optimal in the sense thatit is possible to obtain the same local asymptotic power as we would obtain if thebreakpoint was known. In addition, when observations used to estimate the breakpointare not re-used for the testing, it is possible to use Monte Carlo methods to control sizeperfectly. In contrast to the Sup-Wald type tests, which have non-standard asymptoticdistributions, we show that our tests are asymptotically distributed Chi-square usingmethods similar to those in Andrews (2004). Additionally, our tests stay asymptoticallyvalid even when the distributional assumption made for the Monte Carlo adjustmentsis incorrect. We illustrate the new test statistics in the univariate context of discountrates and changes in the interest rates, and also in the multivariate setting of theCapital Asset Pricing Model.[...]