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Asymptotic mean‐squared forecast error when an autoregression with linear trend is fitted to data generated by an I(0) or I(1) process

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  • Tae‐Hwan Kim
  • Stephen J. Leybourne
  • Paul Newbold

Abstract

. Assume that a time series is generated by an autoregression which has atmost one unit root. A correctly specified model, including linear time trend, is estimated by ordinary least squares, but no allowance is made for any unit root in the generating process. We investigate the impact of estimation error on the mean‐squared error of forecasts calculated from the fitted model.

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  • 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.
    • Handle: RePEc:bla:jtsera:v:25:y:2004:i:4:p:583-602
    DOI: 10.1111/j.1467-9892.2004.01869.x
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    References listed on IDEAS

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    1. Taku Yamamoto, 1976. "Asymptotic Mean Square Prediction Error for an Autoregressive Model with Estimated Coefficients," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 25(2), pages 123-127, June.
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    5. 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(2), pages 238-256, April.
    6. 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.
    7. Choi, In, 1993. "Asymptotic Normality of the Least-Squares Estimates for Higher Order Autoregressive Integrated Processes with Some Applications," Econometric Theory, Cambridge University Press, vol. 9(2), pages 263-282, April.
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    Cited by:

    1. Hansen, Bruce E., 2010. "Averaging estimators for autoregressions with a near unit root," Journal of Econometrics, Elsevier, vol. 158(1), pages 142-155, September.
    2. Chevillon, Guillaume, 2007. "Inference in the Presence of Stochastic and Deterministic Trends," ESSEC Working Papers DR 07021, ESSEC Research Center, ESSEC Business School.
    3. 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.
    4. Chevillon, Guillaume, 2012. "Local-Explosive Approximations to Null Distributions of the Johansen Cointegration Test, with an Application to Cyclical Concordance in the Euro Area," ESSEC Working Papers WP1210, ESSEC Research Center, ESSEC Business School.

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