Joint detection of structural change and nonstationarity in autoregressions

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Description/Abstract

In this paper we develop a test of the joint null hypothesis of parameter stability and a unit root within an ADF style autoregressive specification whose entire parameter structure is potentially subject to a structural break at an unknown time period. The maintained underlying null model is a linear autoregression with a unit root, stationary regressors and a constant term. As a byproduct of our distribution theory we also obtain the limiting behaviour of a related Wald statistic designed to test solely the null of parameter stability in an environment with a unit root. These distributions are free of nuisance parameters and easily tabulated. The finite sample properties of our tests are subsequently assessed through a series of simulations.