Threshold Autoregressions with a Unit Root
This paper develops an asymptotic theory of inference for a two-regime threshold autoregressive (TAR) model with an autoregressive root which is local-to-unity. We find that the asymptotic null distribution of the Wald test for a threshold is non-standard and mildly dependent on the local-to-unity coefficient. We also study the asymptotic null distribution of the Wald test for an autoregressive unit root, and find that it is non-standard and dependent on the presence of a threshold effect. These tests and distribution theory allow for the joint consideration of non-linearity (thresholds) and non-stationarity (unit roots). Our limit theory is based on a new set of tools which combines unit root asymptotics with empirical process methods. We work with a particular two-parameter empirical processes which converges weakly to a two-parameter Brownian motion. Our limit distributions involve stochastic integrals with respect to this two-parameter process. This theory is entirely new and may find applications in other contexts. We illustrate the methods with an application to the U.S. monthly unemployment rate. We find strong evidence of a threshold effect. The point estimates suggest that in about 80% of the observations, the regression function is close to a driftless I(1) process, and in the other 20% of the observations, the regression function is mean-reverting with an unconditional mean of 5%. While the conventional ADF test for a unit root is quite insignificant, our TAR unit root test is arguably significant, with an asymptotic p-value of 3.5%, suggesting that the unemployment rate follows a stationary TAR process.
|Date of creation:||01 Aug 1997|
|Date of revision:|
|Contact details of provider:|| Postal: |
Web page: http://fmwww.bc.edu/EC/
More information through EDIRC
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Pippenger, Michael K & Goering, Gregory E, 1993. "A Note on the Empirical Power of Unit Root Tests under Threshold Processes," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 55(4), pages 473-81, November.
- Hansen, Bruce E, 1996.
"Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis,"
Econometric Society, vol. 64(2), pages 413-30, March.
- Hansen, B.E., 1991. "Inference when a Nuisance Parameter is Not Identified Under the Null Hypothesis," RCER Working Papers 296, University of Rochester - Center for Economic Research (RCER).
- Tom Doan, . "RATS programs to replicate Hansen's threshold estimation and testing results," Statistical Software Components RTZ00091, Boston College Department of Economics.
- Tom Doan, . "TAR: RATS procedure to estimate a threshold autoregression, tests for threshold effect," Statistical Software Components RTS00209, Boston College Department of Economics.
- Potter, Simon M, 1995.
"A Nonlinear Approach to US GNP,"
Journal of Applied Econometrics,
John Wiley & Sons, Ltd., vol. 10(2), pages 109-25, April-Jun.
- Phillips, P C B, 1987.
"Time Series Regression with a Unit Root,"
Econometric Society, vol. 55(2), pages 277-301, March.
- Tom Doan, . "PPUNIT: RATS procedure to perform Phillips-Perron Unit Root test," Statistical Software Components RTS00160, Boston College Department of Economics.
- Peter C.B. Phillips, 1985. "Time Series Regression with a Unit Root," Cowles Foundation Discussion Papers 740R, Cowles Foundation for Research in Economics, Yale University, revised Feb 1986.
- Neftci, Salih N, 1984. "Are Economic Time Series Asymmetric over the Business Cycle?," Journal of Political Economy, University of Chicago Press, vol. 92(2), pages 307-28, April.
- Beaudry, Paul & Koop, Gary, 1993. "Do recessions permanently change output?," Journal of Monetary Economics, Elsevier, vol. 31(2), pages 149-163, April.
- Hansen, Bruce E, 1997.
"Approximate Asymptotic P Values for Structural-Change Tests,"
Journal of Business & Economic Statistics,
American Statistical Association, vol. 15(1), pages 60-67, January.
- Tom Doan, . "RATS programs to replicate Hansen's examples of Andrews-Ploberger test," Statistical Software Components RTZ00087, Boston College Department of Economics.
- Bruce E. Hansen, 1995. "Approximate Asymptotic P-Values for Structural Change Tests," Boston College Working Papers in Economics 297., Boston College Department of Economics.
- Donald W.K. Andrews & Werner Ploberger, 1992.
"Optimal Tests When a Nuisance Parameter Is Present Only Under the Alternative,"
Cowles Foundation Discussion Papers
1015, Cowles Foundation for Research in Economics, Yale University.
- Andrews, Donald W K & Ploberger, Werner, 1994. "Optimal Tests When a Nuisance Parameter Is Present Only under the Alternative," Econometrica, Econometric Society, vol. 62(6), pages 1383-1414, November.
- Bai, Jushan, 1996. "Testing for Parameter Constancy in Linear Regressions: An Empirical Distribution Function Approach," Econometrica, Econometric Society, vol. 64(3), pages 597-622, May.
- Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-84, March.
- Nathan S. Balke & Thomas B. Fomby, 1992.
9209, Federal Reserve Bank of Dallas.
- Robert B. Davies, 2002. "Hypothesis testing when a nuisance parameter is present only under the alternative: Linear model case," Biometrika, Biometrika Trust, vol. 89(2), pages 484-489, June.
- Galbraith, John W, 1996. "Credit Rationing and Threshold Effects in the Relation between Money and Output," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(4), pages 419-29, July-Aug..
When requesting a correction, please mention this item's handle: RePEc:boc:bocoec:381. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Christopher F Baum)
If references are entirely missing, you can add them using this form.