Testing for linear and threshold cointegration under the spatial equilibrium condition

Economic theory states that the spatial equilibrium condition is a region where prices can be or not cointegrated. It is when prices are within such a region when they are no cointegrated, when prices are in its boundaries they are not only cointegrated but also fulfilling the Law of One Price (LOP). Nonetheless the econometric techniques assume a mean reverting process in order to test for cointegration, either linear or non linear. This research shows that in the absence of such mean reverting process by using prices in pure equilibrium, cointegration (linear and non linear) is often rejected. Such findings go in line with the Band Threshold Autoregressive Model where the neutral band is a region of no cointegration. Furthermore it can be concluded that the economic concept of perfect market integration (LOP) by itself is not sufficient for testing cointegration with some of the current econometric methods.