Multiple Structural Changes with Deterministic and Stochastic Trends

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In previous work, we provided a comprehensive treatment of issues related to multiple structural changes in the linear model with stationary or deterministically trending variables. This proposal addresses issues related to multiple structural changes for the empirically important cases where the individual variables are possibly integrated and a system of variables is possibly cointegrated. The presence of integrated variables requires a drastically different theoretical apparatus and poses serious difficulties in the testing strategies to be adopted. This is due to the fact that the limit distributions depend on whether or not a unit root is present but, at the same time, inference about the presence of a unit root depends on whether structural changes are present. Hence, a joint approach is needed. The issues to be tackled will be new theoretical results as well as more practical aspects including extensive simulations about the adequacy of the procedures in finite samples. The research will analyze the consistency of estimated break dates given changes in the slope of a trend function for a univariate integrated series. This is expected to yield more powerful procedures since on ecan then test for a unit root using critical values corresponding to the case of a known break date. The planned research includes the development of tests for structural changes in the trend function of a univariate time series that are valid whether a unit root is present or not. For the multivariate case, research will address the consistency of the break point estimates (whether in the deterministic components or the cointegration vectors); tests for the presence of structural change being agnostic about the number of cointegrating vectors; and tests for the number of cointegrating vectors allowing for multiple structural changes. In this multivariate case, we intend to generalize the univariate Modified AIC for choice of lag length. Finally, we intend to develop an efficient estimation procedure for cases in which other methods for constructing estimates of the break dates will break downIn all the research topics described, we intend to provide applied researchers with a comprehensive set of tools and all procedures will be made available in a Gauss program that will be distributed on request.