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Forecasting Dynamic Time Series in the Presence of Deterministic Components

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  • Serena Ng

    (Boston College)

  • Timothy Vogelsang

    (Cornell University)

Abstract

This paper studies the error in forecasting a dynamic time series with a deterministic component. We show that when the data are strongly serially correlated, forecasts based on a model which detrends the data before estimating the dynamic parameters are much less precise than those based on an autoregression that includes the deterministic components. The local asymptotic distribution of the forecast errors under the two-step procedure exhibits bimodality, and the forecasts are conditionally median biased in a direction that depends on the order of the deterministic trend function. We explore the conditions under which feasible GLS detrending can lead to forecast error reduction. The finite sample properties of OLS and feasible GLS forecasts are compared with forecasts based on unit root pretesting. The procedures are applied to fifteen macroeconomic time series to obtain real time forecasts. Forecasts based on feasible GLS detrending tend to be more efficient than forecasts based on OLS detrending. Regardless of the detrending method, unit root pretests often improve forecasts.

Suggested Citation

  • Serena Ng & Timothy Vogelsang, 1999. "Forecasting Dynamic Time Series in the Presence of Deterministic Components," Boston College Working Papers in Economics 445, Boston College Department of Economics.
    • Handle: RePEc:boc:bocoec:445
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    References listed on IDEAS

    as
    1. John Y. Campbell & Pierre Perron, 1991. "Pitfalls and Opportunities: What Macroeconomists Should Know about Unit Roots," NBER Chapters, in: NBER Macroeconomics Annual 1991, Volume 6, pages 141-220, National Bureau of Economic Research, Inc.
    2. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-836, July.
    3. Peter C.B. Phillips & Chin Chin Lee, 1996. "Efficiency Gains from Quasi-Differencing Under Nonstationarity," Cowles Foundation Discussion Papers 1134, Cowles Foundation for Research in Economics, Yale University.
    4. Elliott, Graham, 1999. "Efficient Tests for a Unit Root When the Initial Observation Is Drawn from Its Unconditional Distribution," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(3), pages 767-783, August.
    5. Diebold, Francis X & Kilian, Lutz, 2000. "Unit-Root Tests Are Useful for Selecting Forecasting Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(3), pages 265-273, July.
    6. Phillips, Peter C. B., 1998. "Impulse response and forecast error variance asymptotics in nonstationary VARs," Journal of Econometrics, Elsevier, vol. 83(1-2), pages 21-56.
    7. Timothy J. Vogelsang, 1998. "Trend Function Hypothesis Testing in the Presence of Serial Correlation," Econometrica, Econometric Society, vol. 66(1), pages 123-148, January.
    8. Eugene Canjels & Mark W. Watson, 1997. "Estimating Deterministic Trends In The Presence Of Serially Correlated Errors," The Review of Economics and Statistics, MIT Press, vol. 79(2), pages 184-200, May.
    9. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    10. Stock, James H, 1996. "VAR, Error Correction and Pretest Forecasts at Long Horizons," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 58(4), pages 685-701, November.
    11. James H. Stock & Mark W. Watson, 1998. "A Comparison of Linear and Nonlinear Univariate Models for Forecasting Macroeconomic Time Series," NBER Working Papers 6607, National Bureau of Economic Research, Inc.
    12. 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.
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    More about this item

    Keywords

    forecasting; trends; unit root; GLS detrending;
    All these keywords.

    JEL classification:

    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling

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