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Path forecast evaluation

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  • �scar Jord�

    (Department of Economics, University of California, Davis, CA, USA)

  • Massimiliano Marcellino

    (Department of Economics, European University Institute, Florence, Italy and Bocconi University)

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 S-method of 1953. 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 the mark. The paper showcases these methods with an application to the most recent monetary episode of interest rate hikes in the US macroeconomy. Copyright © 2010 John Wiley & Sons, Ltd.

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File URL: http://hdl.handle.net/10.1002/jae.1166
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Bibliographic Info

Article provided by John Wiley & Sons, Ltd. in its journal Journal of Applied Econometrics.

Volume (Year): 25 (2010)
Issue (Month): 4 ()
Pages: 635-662

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Handle: RePEc:jae:japmet:v:25:y:2010:i:4:p:635-662

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  1. �scar Jordà, 2009. "Simultaneous Confidence Regions for Impulse Responses," The Review of Economics and Statistics, MIT Press, vol. 91(3), pages 629-647, August.
  2. 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.
  3. James H. Stock & Mark W. Watson, 2001. "Vector Autoregressions," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 101-115, Fall.
  4. Giacomini, Raffaella & White, Halbert, 2003. "Tests of Conditional Predictive Ability," University of California at San Diego, Economics Working Paper Series qt5jk0j5jh, Department of Economics, UC San Diego.
  5. 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, 07.
  6. 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.
  7. Eric M. Leeper & Tao Zha, 2002. "Modest Policy Interventions," NBER Working Papers 9192, National Bureau of Economic Research, Inc.
  8. 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.
  9. 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.
  10. 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.
  11. 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.
  12. M. Hashem Pesaran, 2000. "Forecast Uncertainties in Macroeconometric Modelling: An Application to the UK Economy," CESifo Working Paper Series 345, CESifo Group Munich.
  13. 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.
  14. 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.
  15. 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.
  16. Silvia Goncalves & Lutz Kilian, 2007. "Asymptotic and Bootstrap Inference for AR(∞) Processes with Conditional Heteroskedasticity," Econometric Reviews, Taylor and Francis Journals, vol. 26(6), pages 609-641.
  17. 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.
  18. Guerron-Quintana, Pablo A. & Inoue, Atsushi & Kilian, Lutz, 2009. "Frequentist Inference in Weakly Identified DSGE Models," CEPR Discussion Papers 7447, C.E.P.R. Discussion Papers.
  19. Daniel F. Waggoner & Tao Zha, 1998. "Conditional forecasts in dynamic multivariate models," Working Paper 98-22, Federal Reserve Bank of Atlanta.
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Cited by:
  1. Chevillon, Guillaume, 2009. "Multi-step forecasting in emerging economies: An investigation of the South African GDP," International Journal of Forecasting, Elsevier, vol. 25(3), pages 602-628, July.
  2. Helmut Lütkepohl & Anna Staszewska-Bystrova & Peter Winker, 2013. "Comparison of Methods for Constructing Joint Confidence Bands for Impulse Response Functions," MAGKS Papers on Economics 201325, Philipps-Universität Marburg, Faculty of Business Administration and Economics, Department of Economics (Volkswirtschaftliche Abteilung).
  3. 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.

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