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Inference in the Presence of Stochastic and Deterministic Trends

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Abstract

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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Bibliographic Info

Paper provided by ESSEC Research Center, ESSEC Business School in its series ESSEC Working Papers with number DR 07021.

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Length: 42 pages
Date of creation: Aug 2007
Date of revision:
Handle: RePEc:ebg:essewp:dr-07021

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Postal: ESSEC Research Center, BP 105, 95021 Cergy, France
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Web page: http://www.essec.edu/
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Keywords: Block Local Models; Cointegration; Finite Samples; Likelihood Ratio; Weak Trends;

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  1. 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.
  2. King, Robert G. & Plosser, Charles I. & Stock, James H. & Watson, Mark W., 1991. "Stochastic Trends and Economic Fluctuations," American Economic Review, American Economic Association, vol. 81(4), pages 819-40, September.
  3. 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.
  4. 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.
  5. Chang, Yoosoon & Park, Joon Y. & Song, Kevin, 2006. "Bootstrapping cointegrating regressions," Journal of Econometrics, Elsevier, vol. 133(2), pages 703-739, August.
  6. Fabio Busetti & Andrew Harvey, 2007. "Testing for trend," Temi di discussione (Economic working papers) 614, Bank of Italy, Economic Research and International Relations Area.
  7. Murray, Christian J. & Nelson, Charles R., 2000. "The uncertain trend in U.S. GDP," Journal of Monetary Economics, Elsevier, vol. 46(1), pages 79-95, August.
  8. Evans, G B A & Savin, N E, 1984. "Testing for Unit Roots: 2," Econometrica, Econometric Society, vol. 52(5), pages 1241-69, September.
  9. 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.
  10. Johansen, S., 1999. "A Small Sample Correction for Tests of Hypotheses on the Cointegrating Vectors," Economics Working Papers eco99/9, European University Institute.
  11. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
  12. 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.
  13. 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.
  14. 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.
  15. 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.
  16. 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.
  17. repec:cup:etheor:v:10:y:1994:i:5:p:937-66 is not listed on IDEAS
  18. 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.
  19. 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.
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