DISCUSSION PAPERS IN ECONOMICS AND ECONOMETRICS
Abstract
Discussion Paper No. 1102
Joint Detection of Structural Change and Nonstationarity in Autoregressions
By
Jean-Yves Pitarakis
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. We derive the limiting distribution
of a Supremum Wald type test statistic and show that it can be expressed as the sum of two components each corresponding to the nonstationary and stationary regressors respectively. As a byproduct we also obtain the limiting behaviour of a related Wald statistic designed to solely test 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.
Keywords: Structural Breaks, Unit Roots, Nonlinear Dynamics