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Published online by Cambridge University Press:  13 March 2015

Zhipeng Liao*
UC Los Angeles
Peter C. B. Phillips
Yale University, University of Auckland, University of Southampton, and Singapore Management University
*Address correspondence to Zhipeng Liao, Department of Economics, UC Los Angeles, 8379 Bunche Hall, Mail Stop: 147703, Los Angeles, CA 90095; e-mail:


Model selection and associated issues of post-model selection inference present well known challenges in empirical econometric research. These modeling issues are manifest in all applied work but they are particularly acute in multivariate time series settings such as cointegrated systems where multiple interconnected decisions can materially affect the form of the model and its interpretation. In cointegrated system modeling, empirical estimation typically proceeds in a stepwise manner that involves the determination of cointegrating rank and autoregressive lag order in a reduced rank vector autoregression followed by estimation and inference. This paper proposes an automated approach to cointegrated system modeling that uses adaptive shrinkage techniques to estimate vector error correction models with unknown cointegrating rank structure and unknown transient lag dynamic order. These methods enable simultaneous order estimation of the cointegrating rank and autoregressive order in conjunction with oracle-like efficient estimation of the cointegrating matrix and transient dynamics. As such they offer considerable advantages to the practitioner as an automated approach to the estimation of cointegrated systems. The paper develops the new methods, derives their limit theory, discusses implementation, reports simulations, and presents an empirical illustration with macroeconomic aggregates.

Copyright © Cambridge University Press 2015 

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Comments from two referees and the Co-Editor helped guide the revision of this paper and are gratefully acknowledged. Support from the NSF under Grant Nos. SES 09-56687 and SES 12-58258 is gratefully acknowledged.


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