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This paper studies the properties of maximum likelihood estimates of co-integrated systems. Alternative formulations of such models are considered including a new triangular system error correction mechanism. It is shown that full system maximum likelihood brings the problem of inference within the family that is covered by the locally asymptotically mixed normal asymptotic theory provided that all unit roots in the system have been eliminated by speciﬁcation and data transformation. This result has far reaching consequences. It means that cointegrating coeﬀicient estimates are symmetrically distributed and median unbiased asymptotically, that an optimal asymptotic theory of inference applies and that hypothesis tests may be conducted using standard asymptotic chi-squared sets.
Phillips, Peter C.B., "Optimal Inference in Cointegrated Systems" (1988). Cowles Foundation Discussion Papers. 1109.