Testing for Stationarity and Cointegration in an Unobserved Components Framework
AbstractWhile tests for unit roots and cointegration have important econometric and economic implications, they do not always offer conclusive results. For example, Rudebusch (1992; 1993) demonstrates that standard unit root tests have low power against estimated trend stationary alternatives. In addition, Perron (1989) shows that standard unit root tests cannot always distinguish unit root from stationary processes that contain segmented or shifted trends. Recent research (Harvey 1993; Engel and Morley 2001; Morley, Nelson et al. 2003; Morley 2004; Sinclair 2004) suggests that unobserved components models can provide a useful framework for representing economic time series which contain unit roots, including those that are cointegrated. These series can be modeled as containing an unobserved permanent component, representing the stochastic trend, and an unobserved transitory component, representing the stationary component of the series. These unobserved components are then estimated using the Kalman filter. The unobserved components framework can also provide a more powerful way to test for unit roots and cointegration than what is currently available (Nyblom and Harvey 2000). This paper develops a new test that nests a partial unobserved components model within a more general unobserved components model. This nesting allows the general and the restricted models to be compared using a likelihood ratio test. The likelihood ratio test statistic has a nonstandard distribution, but Monte Carlo simulation can provide its proper distribution. The simulation uses data generated with the results from the partial unobserved components model as the values for the null hypothesis. Consequently, the null hypothesis for this test is stationarity, which is useful in many cases. In this sense our test is like the well-known KPSS test (Kwiatkowski, Phillips et al. 1992), but our test is a parametric version which provides more power by considering the unobserved components structure in calculation of the test statistic. This more powerful test can be used to evaluate important macroeconomic theories such as the permanent income hypothesis, real business cycle theories, and purchasing power parity for exchange rates
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Society for Computational Economics in its series Computing in Economics and Finance 2005 with number 451.
Date of creation: 11 Nov 2005
Date of revision:
unobserved components; unit roots; cointegration;
Find related papers by JEL classification:
- C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models
This paper has been announced in the following NEP Reports:
- NEP-ALL-2005-11-19 (All new papers)
- NEP-ECM-2005-11-19 (Econometrics)
- NEP-ETS-2005-11-19 (Econometric Time Series)
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.:
- Rudebusch, Glenn D, 1993.
"The Uncertain Unit Root in Real GNP,"
American Economic Review,
American Economic Association, vol. 83(1), pages 264-72, March.
- Ralph W. Bailey & A. M. Robert Taylor, 2002.
"An optimal test against a random walk component in a non-orthogonal unobserved components model,"
Royal Economic Society, vol. 5(2), pages 520-532, 06.
- Bailey, R.W. & Taylor, A.M.R., 2000. "An Optimal Test against a Random Walk Component in a Non-Orthogonal Unobserved Components Model," Discussion Papers 00-09, Department of Economics, University of Birmingham.
- Charles Engel & James Morley, 2000.
"The Adjustment of Prices and the Adjustment of the Exchange Rate,"
Discussion Papers in Economics at the University of Washington
0009, Department of Economics at the University of Washington.
- Charles Engel & James C. Morley, 2001. "The Adjustment of Prices and the Adjustment of the Exchange Rate," NBER Working Papers 8550, National Bureau of Economic Research, Inc.
- Charles Engel & James Morley, 2000. "The Adjustment of Prices and the Adjustment of the Exchange Rate," Working Papers 0009, University of Washington, Department of Economics.
- Blanchard, Olivier Jean & Quah, Danny, 1989.
"The Dynamic Effects of Aggregate Demand and Supply Disturbances,"
American Economic Review,
American Economic Association, vol. 79(4), pages 655-73, September.
- Tom Doan, . "BQDODRAWS: RATS procedure to implement Monte Carlo draws from a VAR with Blanchard-Quah factorization," Statistical Software Components RTS00030, Boston College Department of Economics.
- Tom Doan, . "RATS programs to replicate Blanchard and Quah AER 1989," Statistical Software Components RTZ00017, Boston College Department of Economics.
- Olivier Jean Blanchard & Danny Quah, 1990. "The Dynamic Effects of Aggregate Demand and Supply Disturbances," NBER Working Papers 2737, National Bureau of Economic Research, Inc.
- Olivier Jean Blanchard & Danny Quah, 1988. "The Dynamic Effects of Aggregate Demand and Supply Disturbance," Working papers 497, Massachusetts Institute of Technology (MIT), Department of Economics.
- Clark, Peter K., 1989. "Trend reversion in real output and unemployment," Journal of Econometrics, Elsevier, vol. 40(1), pages 15-32, January.
- Grant, Alan P., 2002. "Time-varying estimates of the natural rate of unemployment: a revisitation of Okun's law," The Quarterly Review of Economics and Finance, Elsevier, vol. 42(1), pages 95-113.
- Kwiatkowski, D. & Phillips, P.C.B. & Schmidt, P., 1990.
"Testing the Null Hypothesis of Stationarity Against the Alternative of Unit Root : How Sure are we that Economic Time Series have a Unit Root?,"
8905, Michigan State - Econometrics and Economic Theory.
- Kwiatkowski, Denis & Phillips, Peter C. B. & Schmidt, Peter & Shin, Yongcheol, 1992. "Testing the null hypothesis of stationarity against the alternative of a unit root : How sure are we that economic time series have a unit root?," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 159-178.
- Denis Kwiatkowski & Peter C.B. Phillips & Peter Schmidt, 1991. "Testing the Null Hypothesis of Stationarity Against the Alternative of a Unit Root: How Sure Are We That Economic Time Series Have a Unit Root?," Cowles Foundation Discussion Papers 979, Cowles Foundation for Research in Economics, Yale University.
- repec:cup:etheor:v:6:y:1990:i:4:p:433-44 is not listed on IDEAS
- Perron, P, 1988.
"The Great Crash, The Oil Price Shock And The Unit Root Hypothesis,"
338, Princeton, Department of Economics - Econometric Research Program.
- Perron, Pierre, 1989. "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 57(6), pages 1361-1401, November.
- Glenn D. Rudebusch, 1990.
"Trends and random walks in macroeconomic time series: a re-examination,"
Working Paper Series / Economic Activity Section
105, Board of Governors of the Federal Reserve System (U.S.).
- Rudebusch, Glenn D, 1992. "Trends and Random Walks in Macroeconomic Time Series: A Re-examination," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 33(3), pages 661-80, August.
- Glenn D. Rudebusch, 1990. "Trends and random walks in macroeconomic time series: a re-examination," Finance and Economics Discussion Series 139, Board of Governors of the Federal Reserve System (U.S.).
- Robert G. King & Charles I. Plosser & James H. Stock & Mark W. Watson, 1991.
"Stochastic trends and economic fluctuations,"
Working Paper Series, Macroeconomic Issues
91-4, Federal Reserve Bank of Chicago.
- Harvey, A C, 1985. "Trends and Cycles in Macroeconomic Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 3(3), pages 216-27, June.
- Tanaka, Katsuto, 1990. "Testing for a Moving Average Unit Root," Econometric Theory, Cambridge University Press, vol. 6(04), pages 433-444, December.
- Clark, Peter K, 1987. "The Cyclical Component of U.S. Economic Activity," The Quarterly Journal of Economics, MIT Press, vol. 102(4), pages 797-814, November.
- Robert J. Gordon, 1997.
"The Time-Varying NAIRU and Its Implications for Economic Policy,"
Journal of Economic Perspectives,
American Economic Association, vol. 11(1), pages 11-32, Winter.
- Gordon, Robert J, 1996. "The Time-varying NAIRU and its Implications for Economic Policy," CEPR Discussion Papers 1492, C.E.P.R. Discussion Papers.
- Robert J. Gordon, 1997. "The Time-Varying NAIRU and its Implications for Economic Policy," NBER Working Papers 5735, National Bureau of Economic Research, Inc.
- James C. Morley, 2007. "The Slow Adjustment of Aggregate Consumption to Permanent Income," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(2-3), pages 615-638, 03.
- Christoph Schleicher, 2003. "Structural Time-Series Models with Common Trends and Common Cycles," Computing in Economics and Finance 2003 108, Society for Computational Economics.
- Salemi, Michael K, 1999. "Estimating the Natural Rate of Unemployment and Testing the Natural Rate Hypothesis," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(1), pages 1-25, Jan.-Feb..
- Busetti, Fabio & Harvey, Andrew, 2008.
"Testing For Trend,"
Cambridge University Press, vol. 24(01), pages 72-87, February.
- Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, vol. 10(2), pages 139-162.
- Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July.
- Mehmet Caner & Bruce E. Hansen, 2001.
"Threshold Autoregression with a Unit Root,"
Econometric Society, vol. 69(6), pages 1555-1596, November.
- Nyblom, Jukka & Harvey, Andrew, 1999.
"Tests of Common Stochastic Trends,"
Cambridge Working Papers in Economics
9902, Faculty of Economics, University of Cambridge.
- James C. Morley & Charles R. Nelson & Eric Zivot, 2003.
"Why Are the Beveridge-Nelson and Unobserved-Components Decompositions of GDP So Different?,"
The Review of Economics and Statistics,
MIT Press, vol. 85(2), pages 235-243, May.
- Tom Doan, . "RATS programs to replicate Morley-Nelson-Zivot state space decomposition," Statistical Software Components RTZ00115, Boston College Department of Economics.
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.