Cointegration and distance between differenced processes

In this note, it is argued that cointegration augments the distance between the differenced series. If two series, x <Subscript> t </Subscript> and y <Subscript> t </Subscript>, are integrated of order one and cointegrated and v <Subscript> t </Subscript> and w <Subscript> t </Subscript> are integrated of order one but not cointegrated then, under certain conditions, the distance between Δx <Subscript> t </Subscript> and Δy <Subscript> t </Subscript> is more than the distance between Δv <Subscript> t </Subscript> and Δw <Subscript> t </Subscript>. Copyright Springer Science+Business Media B.V. 2012