THE ASYMPTOTICS OF SINGLE-EQUATION COINTEGRATION REGRESSIONS WITH I(1) AND I(2) VARIABLES

This paper addresses single-equation regression models containing both I(1) and I(2) variables, possibly with maintained deterministic components. We analyze conditions under which standard Gaussian inference can be validly conducted and the existing literature on spurious regressions for the I(1) case is extended to models with I(2) series. The analysis helps in describing how the residual-based Dickey-Fuller class of tests for noncointegration is affected when both I(1) and I(2) variables may enter the system. New critical values for this case are provided. The paper is completed by an empirical application of money demand in the UK.