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Direct and iterated multistep AR methods for difference stationary processes

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  • Proietti, Tommaso

Abstract

The paper focuses on a comparison between the direct and iterated AR predictors for difference stationary processes. In particular, it provides new methods for comparing the efficiency of the two predictors. The methods are based on an encompassing representation for the two predictors, which enables us to derive their properties quite easily under a maintained model. The paper provides an analytical expression for the mean square forecast error of the two predictors and derives useful recursive formulae for computing the direct and iterated coefficients. From an 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 are obtained using the bootstrap method.

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Bibliographic Info

Article provided by Elsevier in its journal International Journal of Forecasting.

Volume (Year): 27 (2011)
Issue (Month): 2 ()
Pages: 266-280

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Handle: RePEc:eee:intfor:v:27:y:2011:i:2:p:266-280

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Web page: http://www.elsevier.com/locate/ijforecast

Related research

Keywords: Multistep estimation; Tapered Yule-Walker estimates; Forecast evaluation;

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References

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  1. 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.
  2. 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.
  3. Guillaume Chevillon, 2005. "Direct multi-step estimation and forecasting," Documents de Travail de l'OFCE 2005-10, Observatoire Francais des Conjonctures Economiques (OFCE).
  4. Marcellino, Massimiliano & Stock, James H. & Watson, Mark W., 2006. "A comparison of direct and iterated multistep AR methods for forecasting macroeconomic time series," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 499-526.
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  8. 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.
  9. Peter M Robinson & Carlos Velasco, 2000. "Whittle Pseudo-Maximum Likelihood Estimation for Nonstationary Time Series - (Now published in Journal of the American Statistical Association, 95, (2000), pp.1229-1243.)," STICERD - Econometrics Paper Series /2000/391, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  10. 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.
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  12. Weiss, Andrew A., 1991. "Multi-step estimation and forecasting in dynamic models," Journal of Econometrics, Elsevier, vol. 48(1-2), pages 135-149.
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Cited by:
  1. McElroy, Tucker & Wildi, Marc, 2013. "Multi-step-ahead estimation of time series models," International Journal of Forecasting, Elsevier, vol. 29(3), pages 378-394.
  2. Chevillon, Guillaume, 2009. "Multi-step forecasting in emerging economies: An investigation of the South African GDP," International Journal of Forecasting, Elsevier, vol. 25(3), pages 602-628, July.

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