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Multi-step ahead forecasting of vector time series

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  • Tucker S. McElroy
  • Michael W. McCracken

Abstract

This paper develops the theory of multi-step ahead forecasting for vector time series that exhibit temporal nonstationarity and co-integration. We treat the case of a semi-infinite past, developing the forecast filters and the forecast error filters explicitly, and also provide formulas for forecasting from a finite-sample of data. This latter application can be accomplished by the use of large matrices, which remains practicable when the total sample size is moderate. Expressions for Mean Square Error of forecasts are also derived, and can be implemented readily. Three diverse data applications illustrate the flexibility and generality of these formulas: forecasting Euro Area macroeconomic aggregates; backcasting fertility rates by racial category; and forecasting regional housing starts using a seasonally co-integrated model.

Suggested Citation

  • Tucker S. McElroy & Michael W. McCracken, 2012. "Multi-step ahead forecasting of vector time series," Working Papers 2012-060, Federal Reserve Bank of St. Louis.
  • Handle: RePEc:fip:fedlwp:2012-060
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    References listed on IDEAS

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    1. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 39(3), pages 106-135.
    2. Nyblom, Jukka & Harvey, Andrew, 2000. "Tests Of Common Stochastic Trends," Econometric Theory, Cambridge University Press, vol. 16(02), pages 176-199, April.
    3. Boubacar Mainassara, Y. & Francq, C., 2011. "Estimating structural VARMA models with uncorrelated but non-independent error terms," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 496-505, March.
    4. M. Ruth & K. Donaghy & P. Kirshen, 2006. "Introduction," Chapters,in: Regional Climate Change and Variability, chapter 1 Edward Elgar Publishing.
    5. Tucker S. McElroy & Thomas M. Trimbur, 2012. "Signal extraction for nonstationary multivariate time series with illustrations for trend inflation," Finance and Economics Discussion Series 2012-45, Board of Governors of the Federal Reserve System (U.S.).
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    Cited by:

    1. Chevillon, Guillaume, 2016. "Multistep forecasting in the presence of location shifts," International Journal of Forecasting, Elsevier, vol. 32(1), pages 121-137.

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    Keywords

    Econometric models ; Economic forecasting;

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