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Evaluating the accuracy of forecasts from vector autoregressions

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  • Todd E. Clark
  • Michael W. McCracken

Abstract

This paper surveys recent developments in the evaluation of point and density forecasts in the context of forecasts made by Vector Autoregressions. Specific emphasis is placed on highlighting those parts of the existing literature that are applicable to direct multi-step forecasts and those parts that are applicable to iterated multi-step forecasts. This literature includes advancements in the evaluation of forecasts in population (based on true, unknown model coefficients) and the evaluation of forecasts in the finite sample (based on estimated model coefficients). The paper then examines in Monte Carlo experiments the finite-sample properties of some tests of equal forecast accuracy, focusing on the comparison of VAR forecasts to AR forecasts. These experiments show the tests to behave as should be expected given the theory. For example, using critical values obtained by bootstrap methods, tests of equal accuracy in population have empirical size about equal to nominal size.

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Bibliographic Info

Paper provided by Federal Reserve Bank of St. Louis in its series Working Papers with number 2013-010.

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Date of creation: 2013
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Handle: RePEc:fip:fedlwp:2013-010

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Keywords: Economic forecasting ; Vector autoregression;

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References

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  1. Kilian, Lutz, 1999. "Exchange Rates and Monetary Fundamentals: What Do We Learn from Long-Horizon Regressions?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(5), pages 491-510, Sept.-Oct.
  2. Clark, Todd E. & West, Kenneth D., 2007. "Approximately normal tests for equal predictive accuracy in nested models," Journal of Econometrics, Elsevier, vol. 138(1), pages 291-311, May.
  3. Todd E. Clark & Kenneth D. West, 2004. "Using out-of-sample mean squared prediction errors to test the Martingale difference hypothesis," Research Working Paper RWP 04-03, Federal Reserve Bank of Kansas City.
  4. Hilde C. Bjørnland & Karsten Gerdrup & Anne Sofie Jore & Christie Smith & Leif Anders Thorsrud, 2012. "Does Forecast Combination Improve Norges Bank Inflation Forecasts?," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 74(2), pages 163-179, 04.
  5. Kadiyala, K. Rao & Karlsson, Sune, 1994. "Numerical Aspects of Bayesian VAR-modeling," Working Paper Series in Economics and Finance 12, Stockholm School of Economics.
  6. Gianni Amisano & Raffaella Giacomini, 2005. "Comparing Density Forecsts via Weighted Likelihood Ratio Tests," Working Papers ubs0504, University of Brescia, Department of Economics.
  7. Clark, Todd E. & McCracken, Michael W., 2001. "Tests of equal forecast accuracy and encompassing for nested models," Journal of Econometrics, Elsevier, vol. 105(1), pages 85-110, November.
  8. Schorfheide, Frank, 2005. "VAR forecasting under misspecification," Journal of Econometrics, Elsevier, vol. 128(1), pages 99-136, September.
  9. Gonçalves, Sílvia & KILIAN, Lutz, 2003. "Bootstrapping Autoregressions with Conditional Heteroskedasticity of Unknown Form," Cahiers de recherche 01-2003, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  10. Berkowitz, Jeremy, 2001. "Testing Density Forecasts, with Applications to Risk Management," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(4), pages 465-74, October.
  11. Domenico Giannone & Michele Lenza & Giorgio E. Primiceri, 2012. "Prior Selection for Vector Autoregressions," NBER Working Papers 18467, National Bureau of Economic Research, Inc.
  12. Gneiting, Tilmann & Raftery, Adrian E., 2007. "Strictly Proper Scoring Rules, Prediction, and Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 359-378, March.
  13. Kenneth Beauchemin & Saeed Zaman, 2011. "A medium scale forecasting model for monetary policy," Working Paper 1128, Federal Reserve Bank of Cleveland.
  14. Todd E. Clark & Michael W. McCracken, 2008. "Tests of equal predictive ability with real-time data," Working Papers 2008-029, Federal Reserve Bank of St. Louis.
  15. Todd E. Clark & Michael W. McCracken, 2008. "Averaging forecasts from VARs with uncertain instabilities," Working Papers 2008-030, Federal Reserve Bank of St. Louis.
  16. Don Coletti & Stephen Murchison, 2002. "Models in Policy-Making," Bank of Canada Review, Bank of Canada, vol. 2002(Spring), pages 19-26.
  17. McCracken, Michael W., 2007. "Asymptotics for out of sample tests of Granger causality," Journal of Econometrics, Elsevier, vol. 140(2), pages 719-752, October.
  18. Carriero, Andrea & Clark, Todd & Marcellino, Massimiliano, 2011. "Bayesian VARs: Specification Choices and Forecast Accuracy," CEPR Discussion Papers 8273, C.E.P.R. Discussion Papers.
  19. Mc Cracken, Michael W., 2000. "Robust out-of-sample inference," Journal of Econometrics, Elsevier, vol. 99(2), pages 195-223, December.
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