Inference in the Presence of Stochastic and Deterministic Trends
The focus of this paper is inference about stochastic and deterministic trends when both types are present. We show that, contrary to asymptotic theory and the existing literature, the parameters of the deterministic components must be taken into account in finite samples. We analyze the ubiquitous Likelihood Ratio test for the rank of cointegration in vector processes. Here, we directly control the parameters of the data generating process so that a local-asymptotic framework accounts for small sample interactions between stochastic and deterministic trends. We show that the usual corrections are invalid as they take no account of the relative magnitudes of these two types of trends. Block-local models provide an embedding framework which provides a rationale for consistent estimation and testing of the whole set of parameters. In an empirical application to European GDP series, we show that using usual corrections leads to underestimating the number of stochastic trends.
|Date of creation:||Aug 2007|
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- Phillips, Peter C.B. & Moon, Hyungsik R., 1999.
"How to Estimate Autoregressive Roots Near Unity,"
University of California at Santa Barbara, Economics Working Paper Series
qt87p2z8zx, Department of Economics, UC Santa Barbara.
- Diebold, Francis X & Senhadji, Abdelhak S, 1996. "The Uncertain Unit Root in Real GNP: Comment," American Economic Review, American Economic Association, vol. 86(5), pages 1291-98, December.
- Douglas Staiger & James H. Stock, 1997.
"Instrumental Variables Regression with Weak Instruments,"
Econometric Society, vol. 65(3), pages 557-586, May.
- Douglas Staiger & James H. Stock, 1994. "Instrumental Variables Regression with Weak Instruments," NBER Technical Working Papers 0151, National Bureau of Economic Research, Inc.
- Busetti, Fabio & Harvey, Andrew, 2008.
"Testing For Trend,"
Cambridge University Press, vol. 24(01), pages 72-87, February.
- Charles Nelson & Christian Murray, 1997.
"The Uncertain Trend in U.S. GDP,"
- Nelson, C-R & Murray, C-J, 1997. "The Uncertain Trend in U.S. GDP," Working Papers 97-05, University of Washington, Department of Economics.
- Chris Murray & Charles Nelson, 1998. "The Uncertain Trend in U.S. GDP," Discussion Papers in Economics at the University of Washington 0074, Department of Economics at the University of Washington.
- Chris Murray & Charles Nelson, 1998. "The Uncertain Trend in U.S. GDP," Working Papers 0074, University of Washington, Department of Economics.
- Nelson, C-R & Murray, C-J, 1997. "The Uncertain Trend in U.S. GDP," Discussion Papers in Economics at the University of Washington 97-05, Department of Economics at the University of Washington.
- 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.
- Johansen, S., 1999.
"A Bartlett Correction Factor for Tests on the Cointegrating Relations,"
Economics Working Papers
eco99/10, European University Institute.
- Johansen, S ren, 2000. "A Bartlett Correction Factor For Tests On The Cointegrating Relations," Econometric Theory, Cambridge University Press, vol. 16(05), pages 740-778, October.
- Chang, Yoosoon & Park, Joon Y. & Song, Kevin, 2006.
"Bootstrapping cointegrating regressions,"
Journal of Econometrics,
Elsevier, vol. 133(2), pages 703-739, August.
- Graham Elliott, 1998. "On the Robustness of Cointegration Methods when Regressors Almost Have Unit Roots," Econometrica, Econometric Society, vol. 66(1), pages 149-158, January.
- Cheung, Yin-Wong & Lai, Kon S, 1993. "Finite-Sample Sizes of Johansen's Likelihood Ration Tests for Conintegration," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 55(3), pages 313-28, August.
- Johansen, Soren, 2002.
"A small sample correction for tests of hypotheses on the cointegrating vectors,"
Journal of Econometrics,
Elsevier, vol. 111(2), pages 195-221, December.
- Johansen, S., 1999. "A Small Sample Correction for Tests of Hypotheses on the Cointegrating Vectors," Economics Working Papers eco99/9, European University Institute.
- Barbara Rossi, 2005.
"Testing Long-Horizon Predictive Ability With High Persistence, And The Meese-Rogoff Puzzle,"
International Economic Review,
Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 46(1), pages 61-92, 02.
- Rossi, Barbara, 2002. "Testing Long-horizon Predictive Ability with High Persistence, and the Meese-Rogoff Puzzle," Working Papers 02-10, Duke University, Department of Economics.
- Jan F. Kiviet & Garry D.A. Phillips, 2001.
"Moment Approximation for Least Squares Estimators in Dynamic Regression Models with a Unit Root,"
Tinbergen Institute Discussion Papers
01-118/4, Tinbergen Institute.
- Kiviet, J.F. & Phillips, G.D.A., 1998. "Moment Approximation for Least Squares Estimators in Dynamic Regression Models with a Unit Root," Discussion Papers 9909, Exeter University, Department of Economics.
- Haldrup, Niels & Hylleberg, Svend, 1995. "A note on the distribution of the least squares estimator of a random walk with drift: Some analytical evidence," Economics Letters, Elsevier, vol. 48(3-4), pages 221-228, June.
- Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-80, November.
- Engle, Robert & Granger, Clive, 2015.
"Co-integration and error correction: Representation, estimation, and testing,"
Publishing House "SINERGIA PRESS", vol. 39(3), pages 106-135.
- Engle, Robert F & Granger, Clive W J, 1987. "Co-integration and Error Correction: Representation, Estimation, and Testing," Econometrica, Econometric Society, vol. 55(2), pages 251-76, March.
- Nabeya, Seiji & Sørensen, Bent E., 1994. "Asymptotic Distributions of the Least-Squares Estimators and Test Statistics in the Near Unit Root Model with Non-Zero Initial Value and Local Drift and Trend," Econometric Theory, Cambridge University Press, vol. 10(05), pages 937-966, December.
- Sampson, Michael, 1991. "The Effect of Parameter Uncertainty on Forecast Variances and Confidence Intervals for Unit Root and Trend Stationary Time-Series Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 6(1), pages 67-76, Jan.-Marc.
- repec:cup:etheor:v:10:y:1994:i:5:p:937-66 is not listed on IDEAS
- Evans, G B A & Savin, N E, 1984. "Testing for Unit Roots: 2," Econometrica, Econometric Society, vol. 52(5), pages 1241-69, September.
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