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Path Forecast Evaluation

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  • Marcellino, Massimiliano
  • Jordà , Ã’scar

Abstract

A path forecast refers to the sequence of forecasts 1 to H periods into the future. A summary of the range of possible paths the predicted variable may follow for a given confidence level requires construction of simultaneous confidence regions that adjust for any covariance between the elements of the path forecast. This paper shows how to construct such regions with the joint predictive density and Scheffé's (1953) S-method. In addition, the joint predictive density can be used to construct simple statistics to evaluate the local internal consistency of a forecasting exercise of a system of variables. Monte Carlo simulations demonstrate that these simultaneous confidence regions provide approximately correct coverage in situations where traditional error bands, based on the collection of marginal predictive densities for each horizon, are vastly off mark. The paper showcases these methods with an application to the most recent monetary episode of interest rate hikes in the U.S. macroeconomy.

Suggested Citation

  • Marcellino, Massimiliano & Jordà , Ã’scar, 2008. "Path Forecast Evaluation," CEPR Discussion Papers 7009, Centre for Economic Policy Research.
    • Handle: RePEc:cpr:ceprdp:7009
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    1. Jean-Marie Dufour & Mohamed Taamouti, 2005. "Projection-Based Statistical Inference in Linear Structural Models with Possibly Weak Instruments," Econometrica, Econometric Society, vol. 73(4), pages 1351-1365, July.
    2. Lütkepohl, Helmut & Poskitt, D.S., 1991. "Estimating Orthogonal Impulse Responses via Vector Autoregressive Models," Econometric Theory, Cambridge University Press, vol. 7(4), pages 487-496, December.
    3. Leeper, Eric M. & Zha, Tao, 2003. "Modest policy interventions," Journal of Monetary Economics, Elsevier, vol. 50(8), pages 1673-1700, November.
    4. Savin, N.E., 1984. "Multiple hypothesis testing," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 14, pages 827-879, Elsevier.
    5. Baillie, Richard T. & Bollerslev, Tim, 1992. "Prediction in dynamic models with time-dependent conditional variances," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 91-113.
    6. Dufour, Jean-Marie, 1990. "Exact Tests and Confidence Sets in Linear Regressions with Autocorrelated Errors," Econometrica, Econometric Society, vol. 58(2), pages 475-494, March.
    7. Bénédicte Vidaillet & V. d'Estaintot & P. Abécassis, 2005. "Introduction," Post-Print hal-00287137, HAL.
    8. Dufour, Jean-Marie, 1989. "Nonlinear Hypotheses, Inequality Restrictions, and Non-nested Hypotheses: Exact Simultaneous Tests in Linear Regressions," Econometrica, Econometric Society, vol. 57(2), pages 335-355, March.
    9. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    10. Silvia Goncalves & Lutz Kilian, 2007. "Asymptotic and Bootstrap Inference for AR(∞) Processes with Conditional Heteroskedasticity," Econometric Reviews, Taylor & Francis Journals, vol. 26(6), pages 609-641.
    11. Kilian, Lutz & Inoue, Atsushi & Guerron-Quintana, Pablo A., 2009. "Frequentist Inference in Weakly Identified DSGE Models," CEPR Discussion Papers 7447, Centre for Economic Policy Research.
    12. James H. Stock & Mark W. Watson, 2001. "Vector Autoregressions," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 101-115, Fall.
    13. Clifford M. Hurvich & Chih‐Ling Tsai, 1993. "A Corrected Akaike Information Criterion For Vector Autoregressive Model Selection," Journal of Time Series Analysis, Wiley Blackwell, vol. 14(3), pages 271-279, May.
    14. Oscar Jorda & Sharon Kozicki, 2007. "Estimation and Inference by the Method of Projection Minimum Distance," Working Papers 148, University of California, Davis, Department of Economics.
    15. Òscar Jordà, 2009. "Simultaneous Confidence Regions for Impulse Responses," The Review of Economics and Statistics, MIT Press, vol. 91(3), pages 629-647, August.
    16. Marcellino, Massimiliano & Stock, James H. & Watson, Mark W., 2006. "A comparison of direct and iterated multistep AR methods for forecasting macroeconomic time series," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 499-526.
    17. Òscar Jordà & Sharon Kozicki, 2007. "Estimation and Inference by the Method of Projection Minimum Distance," Staff Working Papers 07-56, Bank of Canada.
    18. Lewis, Richard & Reinsel, Gregory C., 1985. "Prediction of multivariate time series by autoregressive model fitting," Journal of Multivariate Analysis, Elsevier, vol. 16(3), pages 393-411, June.
    19. Cameron,A. Colin & Trivedi,Pravin K., 2005. "Microeconometrics," Cambridge Books, Cambridge University Press, number 9780521848053.
    20. Raffaella Giacomini & Halbert White, 2006. "Tests of Conditional Predictive Ability," Econometrica, Econometric Society, vol. 74(6), pages 1545-1578, November.
    21. Òscar Jordà, 2005. "Estimation and Inference of Impulse Responses by Local Projections," American Economic Review, American Economic Association, vol. 95(1), pages 161-182, March.
    22. Clements, M.P. & Hendry, D., 1992. "On the Limitations of Comparing Mean Square Forecast Errors," Economics Series Working Papers 99138, University of Oxford, Department of Economics.
    23. M. Hashem Pesaran, 2000. "Forecast Uncertainties in Macroeconometric Modelling: An Application to the UK Economy," CESifo Working Paper Series 345, CESifo.
    24. Daniel F. Waggoner & Tao Zha, 1999. "Conditional Forecasts In Dynamic Multivariate Models," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 639-651, November.
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    Keywords

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    JEL classification:

    • 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
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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