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Direct and iterated multistep AR methods for difference stationary processes

  • Proietti, Tommaso

The paper focuses on the comparison of the direct and iterated AR predictors when Xt is a difference stationary process. In particular, it provides some useful results for comparing the efficiency of the two predictors and for extracting the trend from macroeconomic time series using the two methods. The main results are based on an encompassing representation for the two predictors which enables to derive their properties quite easily under a maintained model. The paper provides an analytic expression for the mean square forecast error of the two predictors and derives useful recursive formulae for computing the direct and iterated coefficients. From the empirical standpoint, we propose estimators of the AR coefficients based on the tapered Yule-Walker estimates; we also provide a test of equal forecast accuracy which is very simple to implement and whose critical values can be obtained with the bootstrap method. Since multistep prediction is tightly bound up with the estimation of the long run component in a time series, we turn to the role of the direct method for trend estimation and derive the corresponding multistep Beveridge-Nelson decomposition.

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File URL: https://mpra.ub.uni-muenchen.de/15343/1/MPRA_paper_15343.pdf
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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 10859.

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Date of creation: 01 Oct 2008
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Handle: RePEc:pra:mprapa:10859
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  1. Weiss, Andrew A., 1991. "Multi-step estimation and forecasting in dynamic models," Journal of Econometrics, Elsevier, vol. 48(1-2), pages 135-149.
  2. Massimiliano Marcellino & James Stock & Mark Watson, 2005. "A Comparison of Direct and Iterated Multistep AR Methods for Forecasting Macroeconomic Time Series," Working Papers 285, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
  3. Clements, Michael P. & Hendry, David F., 1996. "Multi-Step Estimation for Forecasting," The Warwick Economics Research Paper Series (TWERPS) 447, University of Warwick, Department of Economics.
  4. Guillaume Chevillon, 2005. "Direct multi-step estimation and forecasting," Documents de Travail de l'OFCE 2005-10, Observatoire Francais des Conjonctures Economiques (OFCE).
  5. James H. Stock & Mark W. Watson, 2007. "Erratum to "Why Has U.S. Inflation Become Harder to Forecast?"," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(7), pages 1849-1849, October.
  6. repec:cep:stiecm:/2000/391 is not listed on IDEAS
  7. Peter M. Robinson & Carlos Velasco, 2000. "Whittle pseudo-maximum likelihood estimation for nonstationary time series," LSE Research Online Documents on Economics 2273, London School of Economics and Political Science, LSE Library.
  8. Brockwell, P. J. & Dahlhaus, R., 2004. "Generalized Levinson-Durbin and Burg algorithms," Journal of Econometrics, Elsevier, vol. 118(1-2), pages 129-149.
  9. R. Bhansali, 1996. "Asymptotically efficient autoregressive model selection for multistep prediction," Annals of the Institute of Statistical Mathematics, Springer, vol. 48(3), pages 577-602, September.
  10. James H. Stock & Mark W. Watson, 2007. "Why Has U.S. Inflation Become Harder to Forecast?," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(s1), pages 3-33, 02.
  11. Ing, Ching-Kang, 2003. "Multistep Prediction In Autoregressive Processes," Econometric Theory, Cambridge University Press, vol. 19(02), pages 254-279, April.
  12. Proietti, Tommaso & Harvey, Andrew, 2000. "A Beveridge-Nelson smoother," Economics Letters, Elsevier, vol. 67(2), pages 139-146, May.
  13. Zhou, YanYan & Roy, Anindya, 2006. "Effect of tapering on accuracy of forecasts made with stable estimators of vector autoregressive processes," International Journal of Forecasting, Elsevier, vol. 22(1), pages 169-180.
  14. Clive W. J. Granger & Yongil Jeon, 2006. "Dynamics of Model Overfitting Measured in terms of Autoregressive Roots," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(3), pages 347-365, 05.
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