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Multi-step ahead forecasting of vector time series

  • Tucker McElroy
  • Michael W. McCracken

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.

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File URL: http://research.stlouisfed.org/wp/2012/2012-060.pdf
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Paper provided by Federal Reserve Bank of St. Louis in its series Working Papers with number 2012-060.

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Date of creation: 2012
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Handle: RePEc:fip:fedlwp:2012-060
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  1. Engle, Robert F & Granger, Clive W J, 1987. "Co-integration and Error Correction: Representation, Estimation, and Testing," Econometrica, Econometric Society, vol. 55(2), pages 251-76, March.
  2. 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.).
  3. Nyblom, Jukka & Harvey, Andrew, 2000. "Tests Of Common Stochastic Trends," Econometric Theory, Cambridge University Press, vol. 16(02), pages 176-199, April.
  4. 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.
  5. M. Ruth & K. Donaghy & P. Kirshen, 2006. "Introduction," Chapters, in: Regional Climate Change and Variability, chapter 1 Edward Elgar.
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