Testing for Stochastic Cointegration and Evidence for Present Value Models

Using the stochastic integration/cointegration framework of Harris, McCabe and Leybourne (2002) we revisit the problem of assessing the empirical evidence for or against the present value class of models in the bond and stock markets. This framework allows for volatility in excess of that catered for by the conventional integration/cointegration paradigm by introducing nonlinear heteroscedasticity. We propose a test for stochastic cointegration against the alternative of no cointegration and a secondary test for stationary cointegration against the heteroscedastic alternative. Asymptotic distributions of these tests under their respective null hypotheses are derived and consistency under their respective alternatives is established. In contrast to conventional cointegration tests, which we show via simulation are unreliable in the presence of the kind of volatility typical of financial data, our tests are able to uncover new cointegration evidence in favour of the present value model, particularly in the bond market.