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Bootstrap joint prediction regions

Author

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  • Michael Wolf
  • Dan Wunderli

Abstract

Many statistical applications require the forecast of a random variable of interest over several periods into the future. The sequence of individual forecasts, one period at a time, is called a path forecast, where the term path refers to the sequence of individual future realizations of the random variable. The problem of constructing a corresponding joint prediction region has been rather neglected in the literature so far: such a region is supposed to contain the entire future path with a prespecified probability. We develop bootstrap methods to construct joint prediction regions. The resulting regions are proven to be asymptotically consistent under a mild high-level assumption. We compare the finitesample performance of our joint prediction regions to some previous proposals via Monte Carlo simulations. An empirical application to a real data set is also provided.

Suggested Citation

  • Michael Wolf & Dan Wunderli, 2012. "Bootstrap joint prediction regions," ECON - Working Papers 064, Department of Economics - University of Zurich, revised May 2013.
    • Handle: RePEc:zur:econwp:064
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    References listed on IDEAS

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    11. Clements, Michael P. & Taylor, Nick, 2001. "Bootstrapping prediction intervals for autoregressive models," International Journal of Forecasting, Elsevier, vol. 17(2), pages 247-267.
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    Cited by:

    1. Anna Staszewska-Bystrova & Peter Winker, 2014. "Measuring Forecast Uncertainty of Corporate Bond Spreads by Bonferroni-Type Prediction Bands," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 6(2), pages 89-104, June.
    2. Fady Barsoum, 2015. "Point and Density Forecasts Using an Unrestricted Mixed-Frequency VAR Model," Working Paper Series of the Department of Economics, University of Konstanz 2015-19, Department of Economics, University of Konstanz.
    3. Régis Barnichon & Geert Mesters, 2020. "Optimal policy perturbations," Economics Working Papers 1716, Department of Economics and Business, Universitat Pompeu Fabra.
    4. Daniel Grabowski & Anna Staszewska-Bystrova & Peter Winker, 2020. "Skewness-adjusted bootstrap confidence intervals and confidence bands for impulse response functions," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(1), pages 5-32, March.
    5. 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.
    6. Maria Lucia Parrella & Giuseppina Albano & Cira Perna & Michele La Rocca, 2021. "Bootstrap joint prediction regions for sequences of missing values in spatio-temporal datasets," Computational Statistics, Springer, vol. 36(4), pages 2917-2938, December.
    7. Andrew Martinez, 2017. "Testing for Differences in Path Forecast Accuracy: Forecast-Error Dynamics Matter," Working Papers (Old Series) 1717, Federal Reserve Bank of Cleveland.
    8. Sílvia Gonçalves & Benoit Perron & Antoine Djogbenou, 2017. "Bootstrap Prediction Intervals for Factor Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(1), pages 53-69, January.
    9. Lütkepohl, Helmut & Staszewska-Bystrova, Anna & Winker, Peter, 2020. "Constructing joint confidence bands for impulse response functions of VAR models – A review," Econometrics and Statistics, Elsevier, vol. 13(C), pages 69-83.
    10. Pan, Li & Politis, Dimitris N., 2016. "Bootstrap prediction intervals for Markov processes," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 467-494.
    11. David Harris & Gael M. Martin & Indeewara Perera & Don S. Poskitt, 2017. "Construction and visualization of optimal confidence sets for frequentist distributional forecasts," Monash Econometrics and Business Statistics Working Papers 9/17, Monash University, Department of Econometrics and Business Statistics.
    12. Farooq Akram & Andrew Binning & Junior Maih, 2016. "Joint Prediction Bands for Macroeconomic Risk Management," Working Papers No 5/2016, Centre for Applied Macro- and Petroleum economics (CAMP), BI Norwegian Business School.
    13. Pan, Li & Politis, Dimitris, 2014. "Bootstrap prediction intervals for Markov processes," University of California at San Diego, Economics Working Paper Series qt7555757g, Department of Economics, UC San Diego.
    14. Winker, Peter & Helmut, Lütkepohl & Staszewska-Bystrova, Anna, 2014. "Confidence Bands for Impulse Responses: Bonferroni versus Wald," VfS Annual Conference 2014 (Hamburg): Evidence-based Economic Policy 100597, Verein für Socialpolitik / German Economic Association.
    15. Jordà, Òscar & Knüppel, Malte & Marcellino, Massimiliano, 2013. "Empirical simultaneous prediction regions for path-forecasts," International Journal of Forecasting, Elsevier, vol. 29(3), pages 456-468.
    16. Régis Barnichon & Geert Mesters, 2020. "A Sufficient Statistics Approach for Macro Policy Evaluation," Working Papers 1171, Barcelona School of Economics.
    17. Antoniadis, Anestis & Brossat, Xavier & Cugliari, Jairo & Poggi, Jean-Michel, 2016. "A prediction interval for a function-valued forecast model: Application to load forecasting," International Journal of Forecasting, Elsevier, vol. 32(3), pages 939-947.
    18. Lütkepohl, Helmut & Staszewska-Bystrova, Anna & Winker, Peter, 2015. "Comparison of methods for constructing joint confidence bands for impulse response functions," International Journal of Forecasting, Elsevier, vol. 31(3), pages 782-798.
    19. Fresoli, Diego E. & Ruiz, Esther, 2016. "The uncertainty of conditional returns, volatilities and correlations in DCC models," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 170-185.
    20. Giovanni Fonseca & Federica Giummolè & Paolo Vidoni, 2021. "A note on simultaneous calibrated prediction intervals for time series," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(1), pages 317-330, March.
    21. 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.
    22. Skrobotov, Anton (Скроботов, Антон) & Turuntseva, Marina (Турунцева, Марина), 2015. "Theoretical Aspects of Modeling of the SVAR [Теоретические Аспекты Моделирования Svar]," Published Papers mak8, Russian Presidential Academy of National Economy and Public Administration.
    23. Paolo Vidoni, 2017. "Improved multivariate prediction regions for Markov process models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 26(1), pages 1-18, March.
    24. Jordà, Òscar & Knüppel, Malte & Marcellino, Massimiliano, 2013. "Empirical simultaneous prediction regions for path-forecasts," International Journal of Forecasting, Elsevier, vol. 29(3), pages 456-468.

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    More about this item

    Keywords

    Generalized error rates; path forecast; simultaneous prediction intervals;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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