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Bootstrap prediction regions for multivariate autoregressive processes

Author

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  • Matteo Grigoletto

    (University of Padua)

Abstract

. Two new methods for improving prediction regions in the context of vector autoregressive (VAR) models are proposed. These methods, which are based on the bootstrap technique, take into account the uncertainty associated with the estimation of the model order and parameters. In particular, by exploiting an independence property of the prediction error, we will introduce a bootstrap procedure that allows for better estimates of the forecasting distribution, in the sense that the variability of its quantile estimators is substantially reduced, without requiring additional bootstrap replications. The proposed methods have a good performance even if the disturbances distribution is not Gaussian. An application to a real data set is presented.

Suggested Citation

  • Matteo Grigoletto, 2005. "Bootstrap prediction regions for multivariate autoregressive processes," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 14(2), pages 179-207, November.
    • Handle: RePEc:spr:stmapp:v:14:y:2005:i:2:d:10.1007_s10260-005-0113-y
    DOI: 10.1007/s10260-005-0113-y
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    Citations

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    Cited by:

    1. 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.
    2. Helmut Lütkepohl & Anna Staszewska-Bystrova & Peter Winker, 2014. "Confidence Bands for Impulse Responses: Bonferroni versus Wald," Discussion Papers of DIW Berlin 1354, DIW Berlin, German Institute for Economic Research.
    3. Anna Staszewska‐Bystrova, 2011. "Bootstrap prediction bands for forecast paths from vector autoregressive models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 30(8), pages 721-735, December.
    4. Diego Fresoli, 2022. "Bootstrap VAR forecasts: The effect of model uncertainties," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 41(2), pages 279-293, March.
    5. 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.
    6. Anna Staszewska-Bystrova, 2009. "Bootstrap Confidence Bands for Forecast Paths," Working Papers 024, COMISEF.
    7. Lütkepohl, Helmut & Staszewska-Bystrova, Anna & Winker, Peter, 2014. "Confidence bands for impulse responses: Bonferroni versus Wald," SFB 649 Discussion Papers 2014-007, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.

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