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.
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- Evans, G B A & Savin, N E, 1984. "Testing for Unit Roots: 2," Econometrica, Econometric Society, vol. 52(5), pages 1241-69, September.
- 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.
- Johansen, S ren, 2000.
"A Bartlett Correction Factor For Tests On The Cointegrating Relations,"
Cambridge University Press, vol. 16(05), pages 740-778, October.
- Johansen, S., 1999. "A Bartlett Correction Factor for Tests on the Cointegrating Relations," Economics Working Papers eco99/10, European University Institute.
- Fabio Busetti & Andrew Harvey, 2007.
"Testing for trend,"
Temi di discussione (Economic working papers)
614, Bank of Italy, Economic Research and International Relations Area.
- Phillips, Peter C.B. & Moon, Hyungsik Roger & Xiao, Zhijie, 2001.
"How To Estimate Autoregressive Roots Near Unity,"
Cambridge University Press, vol. 17(01), pages 29-69, February.
- 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.
- Peter C.B. Phillips & Hyungsik R. Moon & Zhijie Xiao, 1998. "How to Estimate Autoregressive Roots Near Unity," Cowles Foundation Discussion Papers 1191, Cowles Foundation for Research in Economics, Yale University.
- 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.
- 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.
- 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.
- Robert G. King & Charles I. Plosser & James H. Stock & Mark W. Watson, 1987.
"Stochastic Trends and Economic Fluctuations,"
NBER Working Papers
2229, National Bureau of Economic Research, Inc.
- 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.
- 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.
- Charles Nelson & Christian Murray, 1997. "The Uncertain Trend in U.S. GDP," Computational Economics 9702001, EconWPA.
- Nelson, C-R & Murray, C-J, 1997. "The Uncertain Trend in U.S. GDP," Working Papers 97-05, 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- repec:dgr:uvatin:20010118 is not listed on IDEAS
- 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.
- repec:cup:etheor:v:10:y:1994:i:5:p:937-66 is not listed on IDEAS
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