statistic of Robin and Smith [Econometric Theory (2000), 16, 151–175] usage of numerical optimization for the objective function … singular values in Ratsimalahelo [2002, Rank test based on matrix perturbation theory. Unpublished working paper, U ….F.R. Science Economique, University de Franche-Comté]. In the non-stationary cointegration case, the limiting distribution of the …

cointegration are provided. As a first application, we give analyticalcorroboration of the conjecture that the finite sample … coefficient. Hence, the notionof near cointegration helps to bridge the gap between the polar cases ofspurious regression and … cointegration. Secondly, we characterize theproperties of conventional cointegration methods under near cointegration …

. To illustrate the results, we apply the theory to a number of empirically relevant models. …

-Leibler divergence in empirically relevant settings. We illustrate the theory with an application to time-varying volatility models. We …

extreme value theory for describing multivariate tail dependence. The asymptotic properties of the test are provided and a …