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Bootstrap forecast of multivariate VAR models without using the backward representation

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  • Pascual, Lorenzo
  • Fresoli, Diego Eduardo

Abstract

In this paper, we show how to simplify the construction of bootstrap prediction densities in multivariate VAR models by avoiding the backward representation. Bootstrap prediction densities are attractive because they incorporate the parameter uncertainty a any particular assumption about the error distribution. What is more, the construction of densities for more than one-step unknown asymptotically. The main advantage of the new simple without loosing the good performance of bootstrap procedures. Furthermore, by avoiding a backward representation, its asymptotic validity can be proved without relying on the assumption of Gaussian errors as proposed in this paper can be implemented to obtain prediction densities in models without a backward representation as, for example, models with MA components or GARCH disturbances. By comparing the finite sample performance of the proposed procedure with those of alternatives, we show that nothing is lost when using it. Finally, we implement the procedure to obtain prediction regions for US quarterly future inflation, unemployment and GDP growth

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  • Pascual, Lorenzo & Fresoli, Diego Eduardo, 2011. "Bootstrap forecast of multivariate VAR models without using the backward representation," DES - Working Papers. Statistics and Econometrics. WS ws113426, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:ws113426
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    Cited by:

    1. Stefan Bruder, 2014. "Comparing several methods to compute joint prediction regions for path forecasts generated by vector autoregressions," ECON - Working Papers 181, Department of Economics - University of Zurich, revised Dec 2015.
    2. Staszewska-Bystrova Anna, 2013. "Modified Scheffé’s Prediction Bands," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 233(5-6), pages 680-690, October.
    3. Fresoli, Diego & Ruiz, Esther & Pascual, Lorenzo, 2015. "Bootstrap multi-step forecasts of non-Gaussian VAR models," International Journal of Forecasting, Elsevier, vol. 31(3), pages 834-848.
    4. Staszewska-Bystrova, Anna & Winker, Peter, 2013. "Constructing narrowest pathwise bootstrap prediction bands using threshold accepting," International Journal of Forecasting, Elsevier, vol. 29(2), pages 221-233.

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