Testing Stationarity with Unobserved Components Models

38 Pages Posted: 17 Oct 2012 Last revised: 19 Aug 2014

See all articles by James Morley

James Morley

University of Sydney

Irina Panovska

University of Texas at Dallas

Tara M. Sinclair

George Washington University - Department of Economics; George Washington University - Elliott School of International Affairs (ESIA); George Washington University - Institute For International Economic Policy (GWIIEP); George Washington University - Research Program on Forecasting; George Washington University - George Washington Institute of Public Policy (GWIPP); Australian National University (ANU) - Centre for Applied Macroeconomic Analysis (CAMA); Halle Institute for Economic Research

Date Written: August 18, 2014

Abstract

In the aftermath of the global financial crisis, competing measures of the trend in macroeconomic variables such as US real GDP have featured prominently in policy debates. A key question is whether the 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 for 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 US real GDP produces stronger support for the presence of large permanent shocks when using the likelihood ratio test as compared to the standard tests.

Keywords: Stationarity Test, Likelihood Ratio, Unobserved Components, Parametric Bootstrap, Monte Carlo Simulation, Small-Sample Inference

JEL Classification: C12, C15, C22, E23

Suggested Citation

Morley, James and Panovska, Irina and Sinclair, Tara M., Testing Stationarity with Unobserved Components Models (August 18, 2014). UNSW Business School Research Paper No. 2012 ECON 41B. Available at SSRN: https://ssrn.com/abstract=2162268 or http://dx.doi.org/10.2139/ssrn.2162268

James Morley

University of Sydney ( email )

Rm 370 Merewether (H04)
Sydney, NSW 2006 2008
Australia

HOME PAGE: http://https://sites.google.com/site/jamescmorley/

Irina Panovska

University of Texas at Dallas ( email )

2601 North Floyd Road
Richardson, TX 75083
United States

Tara M. Sinclair (Contact Author)

George Washington University - Department of Economics ( email )

2115 G Street NW
Monroe Hall Suite 340
Washington, DC 20052
United States
202-944-7988 (Phone)
202-994-6147 (Fax)

HOME PAGE: http://home.gwu.edu/~tsinc/

George Washington University - Elliott School of International Affairs (ESIA) ( email )

2201 G Street, N.W.
Washington, DC 20052
United States
202-994-7988 (Phone)
202-994-6147 (Fax)

HOME PAGE: http://home.gwu.edu/~tsinc/

George Washington University - Institute For International Economic Policy (GWIIEP) ( email )

1957 E Street, N.W.
Suite 502
Washington, DC 20052
United States

George Washington University - Research Program on Forecasting ( email )

1922 F Street, NW
Old Main, Suite 208
Washington, DC 20052
United States

George Washington University - George Washington Institute of Public Policy (GWIPP) ( email )


United States

Australian National University (ANU) - Centre for Applied Macroeconomic Analysis (CAMA) ( email )

ANU College of Business and Economics
Canberra, Australian Capital Territory 0200
Australia

Halle Institute for Economic Research ( email )

P.O. Box 11 03 61
Kleine Maerkerstrasse 8
D-06017 Halle, 06108
Germany

HOME PAGE: http://www.dpe-halle.de/asp/person.asp?xtr&Lang=e

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