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Path Forecast Evaluation

Listed author(s):
  • Òscar Jordà
  • Massimiliano Marcellino

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.

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Paper provided by European University Institute in its series Economics Working Papers with number ECO2008/34.

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Date of creation: 2008
Handle: RePEc:eui:euiwps:eco2008/34
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  1. Òscar Jordà, 2009. "Simultaneous Confidence Regions for Impulse Responses," The Review of Economics and Statistics, MIT Press, vol. 91(3), pages 629-647, August.
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  5. 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.
  6. Leeper, Eric M. & Zha, Tao, 2003. "Modest policy interventions," Journal of Monetary Economics, Elsevier, vol. 50(8), pages 1673-1700, November.
  7. 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.
  8. Garrat, A. & Lee, K. & Pesaran, M.H. & Shin, Y., 2000. "Forecast Uncertainties in Macroeconometric Modelling: An Application to the UK Economy," Cambridge Working Papers in Economics 0004, Faculty of Economics, University of Cambridge.
  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.
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  11. 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.
  12. 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.
  13. Pablo Guerron-Quintana & Atsushi Inoue & Lutz Kilian, 2009. "Frequentist inference in weakly identified DSGE models," Working Papers 09-13, Federal Reserve Bank of Philadelphia.
  14. 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.
  15. 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.
  16. James H. Stock & Mark W. Watson, 2001. "Vector Autoregressions," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 101-115, Fall.
  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. 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.
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  21. Cameron,A. Colin & Trivedi,Pravin K., 2005. "Microeconometrics," Cambridge Books, Cambridge University Press, number 9780521848053, January.
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