The Tail Behavior of Maximum Likelihood Estimates of Cointegrating Coefficients in Error Correction Models

Peter Phillips

No 999, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: 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 moments in order T-n+r where T is the sample size, n is the total number of variables in the system and r is the dimension of the cointegration space. These results help to explain simulation studies where extreme outliers are found to occur more frequently for the reduced rank regression estimator than for alternative asymptotically efficient procedures that are based on the triangular representation.

Keywords: Maximum likelihood; error correction model; random walk; cointegration; finite sample (search for similar items in EconPapers)
JEL-codes: C13 C22 C51 (search for similar items in EconPapers)
Pages: 13 pages
Date: 1991-10
Note: CFP 864.
References: Add references at CitEc
Citations: View citations in EconPapers (2)

Published in Econometrica (January 1994), 62(1): 73-93

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