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Path Forecast Evaluation

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  • Oscar Jorda
  • Massimiliano Marcellino

    (Department of Economics, University of California Davis)

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 Scheffe'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.

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Bibliographic Info

Paper provided by University of California, Davis, Department of Economics in its series Working Papers with number 85.

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Length: 45
Date of creation: 16 Jul 2008
Date of revision:
Handle: RePEc:cda:wpaper:08-5

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Keywords: path forecast; simultaneous confidence region; error bands;

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References

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  1. Dufour, Jean-Marie, 1990. "Exact Tests and Confidence Sets in Linear Regressions with Autocorrelated Errors," Econometrica, Econometric Society, vol. 58(2), pages 475-94, March.
  2. Jean-Marie Dufour & Mohamed Taamouti, 2003. "Projection-Based Statistical Inference in Linear Structural Models with Possibly Weak Instruments," CIRANO Working Papers 2003s-39, CIRANO.
  3. Pablo Guerron-Quintana & Atsushi Inoue & Lutz Kilian, 2009. "Frequentist inference in weakly identified DSGE models," Working Papers 09-13, Federal Reserve Bank of Philadelphia.
  4. Daniel F. Waggoner & Tao Zha, 1998. "Conditional forecasts in dynamic multivariate models," Working Paper 98-22, Federal Reserve Bank of Atlanta.
  5. 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.
  6. M. Hashem Pesaran, 2000. "Forecast Uncertainties in Macroeconometric Modelling: An Application to the UK Economy," CESifo Working Paper Series 345, CESifo Group Munich.
  7. James H. Stock & Mark W. Watson, 2001. "Vector Autoregressions," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 101-115, Fall.
  8. Raffaella Giacomini & Halbert White, 2003. "Tests of Conditional Predictive Ability," Econometrics 0308001, EconWPA.
  9. Oscar Jorda & Sharon Kozicki, 2007. "Estimation and Inference by the Method of Projection Minimum Distance," Working Papers 78, University of California, Davis, Department of Economics.
  10. �scar Jordà, 2009. "Simultaneous Confidence Regions for Impulse Responses," The Review of Economics and Statistics, MIT Press, vol. 91(3), pages 629-647, August.
  11. Eric M. Leeper & Tao Zha, 2002. "Modest policy interventions," Working Paper 2002-19, Federal Reserve Bank of Atlanta.
  12. 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.
  13. Marcellino, Massimiliano & Stock, James H & Watson, Mark W, 2005. "A Comparison of Direct and Iterated Multistep AR Methods for Forecasting Macroeconomic Time Series," CEPR Discussion Papers 4976, C.E.P.R. Discussion Papers.
  14. 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.
  15. Lütkepohl, Helmut & Poskitt, D.S., 1991. "Estimating Orthogonal Impulse Responses via Vector Autoregressive Models," Econometric Theory, Cambridge University Press, vol. 7(04), pages 487-496, December.
  16. 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.
  17. 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.
  18. 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.
  19. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-38, May.
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Citations

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Cited by:
  1. Òscar Jordá & Malte Knuppel & Massimiliano Marcellino, 2012. "Empirical simultaneous prediction regions for path-forecasts," Working Paper Series 2012-05, Federal Reserve Bank of San Francisco.
  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. Helmut Lütkepohl & Anna Staszewska-Bystrova & Peter Winker, 2013. "Comparison of Methods for Constructing Joint Confidence Bands for Impulse Response Functions," Discussion Papers of DIW Berlin 1292, DIW Berlin, German Institute for Economic Research.
  4. Carson, Richard T. & Cenesizoglu, Tolga & Parker, Roger, 2011. "Forecasting (aggregate) demand for US commercial air travel," International Journal of Forecasting, Elsevier, vol. 27(3), pages 923-941, July.
  5. Anna Staszewska-Bystrova, 2013. "Modified Scheffé’s Prediction Bands," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), Justus-Liebig University Giessen, Department of Statistics and Economics, vol. 233(5-6), pages 680-690, October.
  6. 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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