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`Weak` trends for inference and forecasting in finite samples

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  • Guillaume Chevillon

Abstract

This paper studies the small sample properties of processes which exhibit both a stochastic and a deterministic trend. Whereas for estimation, inference and forecasting purposes the latter asymptotically dominates the former, it is not so when only a finite number of observations is available and large non-linearities in the parameters of the process result. To analyze this dependence, we resort to local-asymptotics and present the concept of a `weak` trend whose coefficient is of order O(T-1/2), so that the deterministic trend is O(T1/2) and the process Op(T1/2). In this framework, parameter estimates, unit-root test statistics and forecast errors are functions of `drifting` Ornstein-Uhlenbeck processes. We derive a comparison of direct and iterated multi-step estimation and forecasting of a - potentially misspecified - random walk with drift, and show that we explain well the non-linearities exhibited in finite samples. Another main benefit of direct multi-step estimation stems from some different behaviors of the `multi-step` unit-root and slope tests under the weak and strong (constant coefficient) trend frameworks which could lead to testing which framework is more relevant. A Monte Carlo analysis validates the local-asymptotics approximation to the distributions of finite sample biases and test statistics.

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File URL: http://www.economics.ox.ac.uk/materials/working_papers/paper210.pdf
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Bibliographic Info

Paper provided by University of Oxford, Department of Economics in its series Economics Series Working Papers with number 210.

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Date of creation: 01 Dec 2004
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Handle: RePEc:oxf:wpaper:210

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Keywords: Stochastic Trend; Deterministic Trend; Local Asymptotics; Multi-step Forecasting;

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  1. Banerjee, A & Hendry, D-F & Mizon, G-E, 1996. "The Econometric Analysis of Economic Policy," Economics Working Papers eco96/34, European University Institute.
  2. Diebold & Senhadji, . "Deterministic vs. Stochastic Trend in U.S. GNP, Yet Again," Home Pages _054, University of Pennsylvania.
  3. Peter C.B. Phillips, 2004. "Challenges of Trending Time Series Econometrics," Cowles Foundation Discussion Papers 1472, Cowles Foundation for Research in Economics, Yale University.
  4. Peter C. B. Phillips, 1998. "New Tools for Understanding Spurious Regressions," Econometrica, Econometric Society, vol. 66(6), pages 1299-1326, November.
  5. Phillips, Peter C B, 1988. "Regression Theory for Near-Integrated Time Series," Econometrica, Econometric Society, vol. 56(5), pages 1021-43, September.
  6. Chevillon, Guillaume & Hendry, David F., 2005. "Non-parametric direct multi-step estimation for forecasting economic processes," International Journal of Forecasting, Elsevier, vol. 21(2), pages 201-218.
  7. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
  8. Douglas Staiger & James H. Stock, 1994. "Instrumental Variables Regression with Weak Instruments," NBER Technical Working Papers 0151, National Bureau of Economic Research, Inc.
  9. 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.
  10. Clements, M.P. & Hendry, D.P., 1998. "Forecasting with Difference-Stationary and Trend-Stationary Models," The Warwick Economics Research Paper Series (TWERPS) 516, University of Warwick, Department of Economics.
  11. Kemp, Gordon C.R., 1999. "The Behavior Of Forecast Errors From A Nearly Integrated Ar(1) Model As Both Sample Size And Forecast Horizon Become Large," Econometric Theory, Cambridge University Press, vol. 15(02), pages 238-256, April.
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Cited by:
  1. Guillaume Chevillon, 2004. "A Comparison of Multi-step GDP Forecasts for South Africa," Economics Series Working Papers 212, University of Oxford, Department of Economics.

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