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Estimation And Inference In Models Of Cointegration: A Simulation Study, Bruce E. Hansen, Peter C.B. Phillips
Estimation And Inference In Models Of Cointegration: A Simulation Study, Bruce E. Hansen, Peter C.B. Phillips
Cowles Foundation Discussion Papers
This paper studies the finite sample distributions of estimators of the cointegrating vector of linear regression models with I(1) variables. Attention is concentrated on the least squares (OLS) and instrumental variables (IV) methods analyzed in other recent work (Phillips and Hansen (1988)). The general preference of OLS to IV techniques suggested by asymptotic theory is reinforced by our simulations. An exception arises for cases of low signal to noise, where spurious IV techniques (so named for their use of instruments that are structurally unrelated to the model) outperform uncorrected least squares. We verify the presence of a small sample estimation …
Error Correction And Long Run Equilibrium In Continuous Time, Peter C.B. Phillips
Error Correction And Long Run Equilibrium In Continuous Time, Peter C.B. Phillips
Cowles Foundation Discussion Papers
This paper deals with error correction models (ECM’s) and cointegrated systems that are formulated in continuous time. Problems of representation, identification, estimation and time aggregation are discussed. It is shown that every ECM in continuous time has a discrete time equivalent model in ECM format. Moreover, both models may be written as triangular systems with stationary errors. This formulation simplifies both the continuous and the discrete time ECM representations and it helps to motivate a class of optimal inference procedures. It is further shown that long run equilibria in the continuous system are always identified in the discrete time reduced …
Spectral Regression For Cointegrated Time Series, Peter C.B. Phillips
Spectral Regression For Cointegrated Time Series, Peter C.B. Phillips
Cowles Foundation Discussion Papers
This paper studies the use of spectral regression techniques in the context of cointegrated systems of multiple time series. Several alternatives are considered including efficient and band spectral methods as well as system and single equation techniques. It is shown that single equation spectral regressions suffer asymptotic bias and nuisance parameter problems that render these regressions impotent for inferential purposes. By contrast systems methods are shown to be covered by LAMN asymptotic theory, bringing the advantages of asymptotic media unbiasedness, scale nuisance parameters and the convenience of asymptotic chi-squared tests. System spectral methods also have advantages over full system direct …
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 …