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Multistep ahead forecasting of vector time series

Listed author(s):
  • Tucker McElroy
  • Michael W. McCracken

This article develops the theory of multistep ahead forecasting for vector time series that exhibit temporal nonstationarity and co-integration. We treat the case of a semi-infinite past by developing the forecast filters and the forecast error filters explicitly. We also provide formulas for forecasting from a finite data sample. This latter application can be accomplished by using large matrices, which remains practicable when the total sample size is moderate. Expressions for the mean square error of forecasts are also derived and can be implemented readily. The flexibility and generality of these formulas are illustrated by four diverse applications: forecasting euro area macroeconomic aggregates; backcasting fertility rates by racial category; forecasting long memory inflation data; and forecasting regional housing starts using a seasonally co-integrated model.

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File URL: http://hdl.handle.net/10.1080/07474938.2014.977088
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Article provided by Taylor & Francis Journals in its journal Econometric Reviews.

Volume (Year): 36 (2017)
Issue (Month): 5 (May)
Pages: 495-513

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Handle: RePEc:taf:emetrv:v:36:y:2017:i:5:p:495-513
DOI: 10.1080/07474938.2014.977088
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  1. Nyblom, Jukka & Harvey, Andrew, 2000. "Tests Of Common Stochastic Trends," Econometric Theory, Cambridge University Press, vol. 16(02), pages 176-199, April.
  2. 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.
  3. 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.
  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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