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The Tail Behavior Of Maximum Likelihood Estimates Of Cointegrating Coefficients In Error Correction Models, Peter C.B. Phillips
The Tail Behavior Of Maximum Likelihood Estimates Of Cointegrating Coefficients In Error Correction Models, Peter C.B. Phillips
Cowles Foundation Discussion Papers
This paper derives exact finite sample distributions of maximum likelihood estimators of the cointegrating coefficients in error correction models. The distributions are derived for the leading case where the variables in the system are independent random walks. But important aspects of the theory, in particular the tail behavior of the distributions, continue to apply when the system is cointegrated. The reduced rank regression estimator is shown to have a distribution with Cauchy-like tails and no finite moments of integer order. The maximum likelihood estimator of the coefficients in the triangular system representation has matrix t -distribution tails with finite integer …
Vector Autoregression And Causality, Hiro Y. Toda, Peter C.B. Phillips
Vector Autoregression And Causality, Hiro Y. Toda, Peter C.B. Phillips
Cowles Foundation Discussion Papers
This paper develops a complete limit theory for Wald tests of Granger causality in levels vector autoregression (VAR’s) and Johansen-type error correction models (ECM’s) allowing for the presence of stochastic trends and cointegration. Earlier work by Sims, Stock and Watson (1990) on trivariate VAR systems is extended to the general case, thereby formally characterizing the circumstances when these Wald tests are asymptotically valid as chi-square criteria. Our results for inference from unrestricted levels VAR are not encouraging.