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Time series variables that stochastically trend together form a cointegrated system. OLS and NLS estimators of the parameters of a cointegrating vector are shown to converge in probability to the true parameter value at the rate T11d for any positive d. These estim mators can be written asymptotically in terms of relatively simple nonnormal random matrices which do not depend on the parameters of th e system. These asymptotic representations form the basis for simple and fast Monte Carlo calculations of the limiting distributions of th ese estimators. Asymptotic distributions thus computed are tabulated for several cointegrated processes. Copyright 1987 by The Econometric Society.