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Testing For A Unit Root In The Presence Of A Maintained Trend, Sam Ouliaris, Joon Y. Park, Peter C.B. Phillips
Testing For A Unit Root In The Presence Of A Maintained Trend, Sam Ouliaris, Joon Y. Park, Peter C.B. Phillips
Cowles Foundation Discussion Papers
This paper develops statistics for detecting the presence of a unit root in time series data against the alternative stationarity. Unlike most existing procedures, the new tests allow for deterministic trend polynomials in the maintained hypothesis. They may be used to discriminate between unit root nonstationarity and processes which are stationary around a deterministic polynomial trend. The tests allow for both forms of nonstationarity under the null hypothesis. Moreover, the tests allow for a wide class of weakly dependent and possibly heterogenously distributed procedures. We illustrate the use of the new tests by applying them to a number a models …
Optimal Inference In Cointegrated Systems, Peter C.B. Phillips
Optimal Inference In Cointegrated Systems, Peter C.B. Phillips
Cowles Foundation Discussion Papers
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 …