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TESTING STATIONARITY WITH UNOBSERVED-COMPONENTS MODELS

Published online by Cambridge University Press:  08 March 2016

James Morley ,
Irina B. Panovska  and
Tara M. Sinclair
James Morley
Affiliation:
University of New South Wales
Irina B. Panovska
Affiliation:
Lehigh University
Tara M. Sinclair*
Affiliation:
The George Washington University
*
Address correspondence to: Tara M. Sinclair, Department of Economics, The George Washington University, Monroe Hall # 340, 2115 G Street NW, Washington, DC 20052, USA; e-mail: tsinc@gwu.edu.
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Abstract

In the aftermath of the global financial crisis, competing measures of the trend in macroeconomic variables such as U.S. real GDP have featured prominently in policy debates. A key question is whether large shocks to macroeconomic variables will have permanent effects—i.e., in econometric terms, do the data contain stochastic trends? Unobserved-components models provide a convenient way to estimate stochastic trends for time series data, with their existence typically motivated by stationarity tests that allow at most a deterministic trend under the null hypothesis. However, given the small sample sizes available for most macroeconomic variables, standard Lagrange multiplier tests of stationarity will perform poorly when the data are highly persistent. To address this problem, we propose the use of a likelihood ratio test of stationarity based directly on the unobserved-components models used in estimation of stochastic trends. We demonstrate that a bootstrap version of this test has far better small-sample properties for empirically relevant data-generating processes than bootstrap versions of the standard Lagrange multiplier tests. An application to U.S. real GDP produces stronger support for the presence of large permanent shocks using the likelihood ratio test than using the standard tests.

Keywords

Stationarity TestLikelihood RatioUnobserved ComponentsParametric BootstrapMonte Carlo SimulationSmall-Sample Inference
Type
Articles
Information
Macroeconomic Dynamics , Volume 21 , Issue 1 , January 2017 , pp. 160 - 182
Copyright
Copyright © Cambridge University Press 2016 

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