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Unbiasedness of Predictions From Estimated Vector Autoregressions

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  • Dufour, J.M.

Abstract

Forecasts from a univariate autoregressive model estimated by OLS are unbiased, irrespective of whether the model fitted has the correct order; this property only requires symmetry of the distribution of the innovations. In this paper, this result is generalized to vector autoregressions and a wide class of multivariate stochastic processes (which include Gaussian stationary multivariate stochastic processes) is described for which unbiasedness of predictions holds: specifically, if a vector autoregression of arbitrary finite order is fitted to a sample from any process in this class, the fitted model will produce unbiased forecasts, in the sense that the prediction errors have distributions symmetric about zero. Different numbers of lags may be used for each variable in each autoregression and variables may even be missing, without unbiasedness being affected. This property is exact in finite samples. Similarly, the residuals from the same autoregressions have distributions symmetric about zero.
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Suggested Citation

  • Dufour, J.M., 1983. "Unbiasedness of Predictions From Estimated Vector Autoregressions," Cahiers de recherche 8330, Universite de Montreal, Departement de sciences economiques.
    • Handle: RePEc:mtl:montde:8330
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    Cited by:

    1. Gomez, Nicolas & Guerrero, Victor M., 2006. "Restricted forecasting with VAR models: An analysis of a test for joint compatibility between restrictions and forecasts," International Journal of Forecasting, Elsevier, vol. 22(4), pages 751-770.
    2. Arino, Miguel A. & Franses, Philip Hans, 2000. "Forecasting the levels of vector autoregressive log-transformed time series," International Journal of Forecasting, Elsevier, vol. 16(1), pages 111-116.
    3. Jean Francois David & Eric Ghysels, 1989. "Y a-t-il des biais systematiques dans les annonces budgetaires canadiennes? (With English summary.)," Canadian Public Policy, University of Toronto Press, vol. 15(3), pages 313-321, September.
    4. Steffen Henzel & Johannes Mayr, 2009. "The Virtues of VAR Forecast Pooling – A DSGE Model Based Monte Carlo Study," ifo Working Paper Series 65, ifo Institute - Leibniz Institute for Economic Research at the University of Munich.

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