Likelihood ratio (LR) tests for the cointegrating rank of a vector autoregressive (VAR) process have been developed under different assumptions regarding deterministic terms. For instance, nonzero mean terms and linear trends have been accounted for in some of the tests. In this paper we provide...

Since the 1960s hydrocarbons like crude oil and natural gas have been the most important energy source to fuel the world economy. Despite high recent growth rates for renewable energies, hydro- carbons are expected to be a dominant source of energy for several decades to come. In the last 20...