The Cointegrated VAR Model with Deterministic Structural Breaks

Abstract

The presence of a binary variable in the cointegrated VAR (CVAR) model
is most often interpreted as the structural break affecting the data generating
process. It is proved in the paper that to enjoy this interpretation the binary
variable must appear simultaneously inside and outside the cointegration space.
In order to test for the break we advocate to employ the Wald statistic, however,
its critical values and the power had to be simulated separately for the possible
change of the constant, the trend, and both. The experiments were designed for
different sizes of the cointegrating space, number of variables, the span of the
break, normally and t-distributed errors. It is shown that the power of the test
depends mostly on the magnitude of the break and the sample size while other
factors are of secondary importance. In order to test for the break at unknown
period the supWald statistic was proposed.