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Forecasting Dynamic Time Series in the Presence of Deterministic Components

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Author Info
Serena Ng () (Boston College)
Timothy Vogelsang (Cornell University)

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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.

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Publisher Info
Paper provided by Boston College Department of Economics in its series Boston College Working Papers in Economics with number 445.

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Length: 22 pages
Date of creation: 15 Jul 1999
Date of revision:
Handle: RePEc:boc:bocoec:445

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Related research
Keywords: forecasting; trends; unit root; GLS detrending;

Find related papers by 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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  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. [Downloadable!]
    Other versions:
  2. 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. [Downloadable!] (restricted)
    Other versions:
  3. 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. [Downloadable!] (restricted)
  4. 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. [Downloadable!] (restricted)
  5. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-36, July. [Downloadable!] (restricted)
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  6. Peter C.B. Phillips & Chin Chin Lee, 1996. "Efficiency Gains from Quasi-Differencing Under Nonstationarity," Cowles Foundation Discussion Papers 1134, Cowles Foundation, Yale University. [Downloadable!]
  7. Francis X. Diebold & Lutz Kilian, 1999. "Unit Root Tests Are Useful for Selecting Forecasting Models," NBER Working Papers 6928, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  8. Timothy J. Vogelsang, 1998. "Trend Function Hypothesis Testing in the Presence of Serial Correlation," Econometrica, Econometric Society, vol. 66(1), pages 123-148, January.
  9. 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 767-83, August.
    Other versions:
  10. Diebold, Francis X & Mariano, Roberto S, 1995. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(3), pages 253-63, July.
    Other versions:
  11. 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.
  12. 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. [Downloadable!] (restricted)
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