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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.

Suggested Citation

  • Guillaume Chevillon, 2004. "`Weak` trends for inference and forecasting in finite samples," Economics Series Working Papers 210, University of Oxford, Department of Economics.
  • Handle: RePEc:oxf:wpaper:210
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    File URL: http://www.economics.ox.ac.uk/materials/working_papers/paper210.pdf
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    References listed on IDEAS

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    1. 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.
    2. Phillips, Peter C.B., 2005. "Challenges of trending time series econometrics," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 68(5), pages 401-416.
    3. Michael P. Clements & David F.Hendry, 2001. "Forecasting with difference-stationary and trend-stationary models," Econometrics Journal, Royal Economic Society, vol. 4(1), pages 1-19.
    4. Phillips, Peter C B, 1988. "Regression Theory for Near-Integrated Time Series," Econometrica, Econometric Society, vol. 56(5), pages 1021-1043, September.
    5. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    6. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    7. Diebold & Senhadji, "undated". "Deterministic vs. Stochastic Trend in U.S. GNP, Yet Again," Home Pages _054, University of Pennsylvania.
    8. Banerjee, Anindya & Hendry, David F & Mizon, Grayham E, 1996. "The Econometric Analysis of Economic Policy," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 58(4), pages 573-600, November.
    9. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    10. Peter C. B. Phillips, 1998. "New Tools for Understanding Spurious Regressions," Econometrica, Econometric Society, vol. 66(6), pages 1299-1326, November.
    11. 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.
    12. 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.

    More about this item

    Keywords

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

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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