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The Effect of Parameter Uncertainty on Forecast Variances and Confidence Intervals for Unit Root and Trend Stationary Time-Series Models

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  • Sampson, Michael

Abstract

In this paper I describe the effect of parameter uncertainty on the way conditional forecast variances grow as the forecast horizon increases. Without parameter uncertainty, forecast variances for the unit root model grow linearly with the forecast horizon while with the trend stationary model they are bounded. With parameter uncertainty, however, I find that for both the unit root and the trend stationary models, forecast variances grow with the square of the forecast horizon so that uncertainty grows at a much faster rate than without parameter uncertainty. Copyright 1991 by John Wiley & Sons, Ltd.

Suggested Citation

  • 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.
    • Handle: RePEc:jae:japmet:v:6:y:1991:i:1:p:67-76
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    Citations

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    Cited by:

    1. Tae‐Hwan Kim & Stephen J. Leybourne & Paul Newbold, 2004. "Asymptotic mean‐squared forecast error when an autoregression with linear trend is fitted to data generated by an I(0) or I(1) process," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(4), pages 583-602, July.
    2. Hendry, David F. & Clements, Michael P., 2003. "Economic forecasting: some lessons from recent research," Economic Modelling, Elsevier, vol. 20(2), pages 301-329, March.
    3. 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.
    4. Gospodinov, Nikolay, 2002. "Median unbiased forecasts for highly persistent autoregressive processes," Journal of Econometrics, Elsevier, vol. 111(1), pages 85-101, November.
    5. Sampson, Michael J., 1994. "Precautionary savings and wealth accumulation with parameter uncertainty and learning," ZEW Discussion Papers 94-08, ZEW - Leibniz Centre for European Economic Research.
    6. Guillaume Chevillon, 2004. "`Weak` trends for inference and forecasting in finite samples," Economics Series Working Papers 210, University of Oxford, Department of Economics.
    7. Guillaume Chevillon, 2017. "Robust cointegration testing in the presence of weak trends, with an application to the human origin of global warming," Econometric Reviews, Taylor & Francis Journals, vol. 36(5), pages 514-545, May.
    8. John W. Galbraith, 1999. "Content Horizons for Forecasts of Economic Time Series," CIRANO Working Papers 99s-17, CIRANO.
    9. Chevillon, Guillaume, 2007. "Inference in the Presence of Stochastic and Deterministic Trends," ESSEC Working Papers DR 07021, ESSEC Research Center, ESSEC Business School.
    10. Koop, Gary & Steel, Mark F J, 1994. "A Decision-Theoretic Analysis of the Unit-Root Hypothesis Using Mixtures of Elliptical Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(1), pages 95-107, January.
    11. Farmer, J. Doyne & Lafond, François, 2016. "How predictable is technological progress?," Research Policy, Elsevier, vol. 45(3), pages 647-665.
    12. Lafond, François & Bailey, Aimee Gotway & Bakker, Jan David & Rebois, Dylan & Zadourian, Rubina & McSharry, Patrick & Farmer, J. Doyne, 2018. "How well do experience curves predict technological progress? A method for making distributional forecasts," Technological Forecasting and Social Change, Elsevier, vol. 128(C), pages 104-117.
    13. Sampson, Michael, 2003. "New Eras and Stock Market Bubbles," Structural Change and Economic Dynamics, Elsevier, vol. 14(3), pages 297-315, September.
    14. Koop, Gary & Osiewalski, Jacek & Steel, Mark F. J., 1995. "Bayesian long-run prediction in time series models," Journal of Econometrics, Elsevier, vol. 69(1), pages 61-80, September.
    15. Helmut Lütkepohl, 2010. "Forecasting Aggregated Time Series Variables: A Survey," OECD Journal: Journal of Business Cycle Measurement and Analysis, OECD Publishing, Centre for International Research on Economic Tendency Surveys, vol. 2010(2), pages 1-26.
    16. repec:hal:journl:hal-00914830 is not listed on IDEAS
    17. Ulrich Gunter & Irem Önder & Stefan Gindl, 2019. "Exploring the predictive ability of LIKES of posts on the Facebook pages of four major city DMOs in Austria," Tourism Economics, , vol. 25(3), pages 375-401, May.
    18. Diebold, Francis X. & Lindner, Peter, 1996. "Fractional integration and interval prediction," Economics Letters, Elsevier, vol. 50(3), pages 305-313, March.
    19. Michael Sampson, 2022. "The Effect of Parameter Uncertainty on Consumption, Wealth, and Welfare," Annals of Economics and Finance, Society for AEF, vol. 23(1), pages 1-10, May.
    20. Koop, Gary, 1996. "Parameter uncertainty and impulse response analysis," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 135-149.

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