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Forecasting autoregressive time series in the presence of deterministic components

Author

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  • Serena Ng

    (Department of Economics, Johns Hopkins University, USA)

  • Timothy J. Vogelsang

    (Department of Economics, Cornell University Uris Hall, USA)

Abstract

This paper studies the error in forecasting an autoregressive process with a deterministic component. We show that when the data are strongly serially correlated, forecasts based on a model that detrends the data using OLS before estimating the autoregressive parameters are much less precise than those based on an autoregression that includes the deterministic components, and the asymptotic distribution of the forecast errors under the two-step procedure exhibits bimodality. We explore the conditions under which feasible GLS trend estimation 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 15 macroeconomic time series to obtain real time forecasts. Forecasts based on feasible GLS trend estimation tend to be more efficient than forecasts based on OLS trend estimation. A new finding is when a unit root pretest rejects non-stationarity, use of GLS yields smaller forecast errors than OLS. When the series to be forecasted is highly persistent, GLS trend estimation in conjunction with unit root pretests can lead to sharp reduction in forecast errors. Copyright Royal Economic Society 2002

Suggested Citation

  • Serena Ng & Timothy J. Vogelsang, 2002. "Forecasting autoregressive time series in the presence of deterministic components," Econometrics Journal, Royal Economic Society, vol. 5(1), pages 196-224, June.
    • Handle: RePEc:ect:emjrnl:v:5:y:2002:i:1:p:196-224
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    Cited by:

    1. Mohitosh Kejriwal & Xuewen Yu, 2019. "Generalized Forecasr Averaging in Autoregressions with a Near Unit Root," Purdue University Economics Working Papers 1318, Purdue University, Department of Economics.
    2. Barry K. Goodwin & Matthew T. Holt & Jeffrey P. Prestemon, 2021. "Semi-parametric models of spatial market integration," Empirical Economics, Springer, vol. 61(5), pages 2335-2361, November.
    3. Mynbaev, Kairat, 2003. "Asymptotic properties of OLS estimates in autoregressions with bounded or slowly growing deterministic trends," MPRA Paper 18448, University Library of Munich, Germany, revised 2005.
    4. John L. Turner, 2004. "Local to unity, long-horizon forecasting thresholds for model selection in the AR(1)," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 23(7), pages 513-539.
    5. Falk, Barry & Roy, Anindya, 2005. "Forecasting using the trend model with autoregressive errors," International Journal of Forecasting, Elsevier, vol. 21(2), pages 291-302.

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