It is well known that systems of regression equations exhibiting different characteristics along each equation do not necessarily conform to standard asymptotic theory of estimation and testing. The key difference with the standard asymptotic framework of inference is that sample moment matrices require matrix-valued normalisations, a complication that may result to a reduction in the asymptotic rank of sample moment estimators and the associated test statistics. In hypothesis testing, an additional complication arises from the interaction between the matrix-valued normalisation and the matrix of restrictions imposed by the null hypothesis, which may lead to further asymptotic degeneracy and non-standard limit distributions for Wald type test statistics. The paper provides sufficient conditions that guarantee standard chi-squared inference for the classical trinity of tests in this general multivariate modelling framework. Applications include regression models with deterministic components, cointegrated systems of near-integrated time series with roots that induce potentially different persistence rates and fractionally cointegrated systems.
Professor Anastasios Magdalinos is Professor in Econometrics within Social Sciences: Economics at the University of Southampton. He joined the division in September 2010 having held previous positions at the University of Nottingham and the University of York. His research interests are in the area of time series econometrics with particular focus on investigating boundaries between stationary and non-stationary processes, robust inference in cointegrating and predictive regression, asymptotic theory for nearly unstable processes, explosive processes and bubbles, and long memory processes. He has published in peer-reviewed journals such as Econometric Theory, the Journal of Econometrics, the Econometrics Journal and the Review of Financial Studies. His research has received funding from the ESRC and the British Academy, and he is an associate editor of Econometric Theory and of the Journal of Time Series Analysis.