The asymptotic distribution of the CADF unit root test in the presence of heterogeneous AR(p) errors

The CADF test of Pesaran (J Appl Econ 22:265–312, 2007) are among the most popular univariate tests for cross-section correlated panels around. Yet, the existing asymptotic analysis of this test statistic is limited to a model in which the errors are assumed to follow a simple AR(1) structure with homogenous autoregressive coefficients. One reason for this is that the model involves an intricate identification issue, as both the serial and cross-section correlation structures of the errors are unobserved. The purpose of the current paper is to tackle this issue and in so doing extend the existing analysis to the case of AR((Formula presented.)) errors with possibly heterogeneous coefficients.