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Evaluating the accuracy of forecasts from vector autoregressions

Listed author(s):
  • Todd E. Clark
  • Michael W. McCracken

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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File URL: http://research.stlouisfed.org/wp/2013/2013-010.pdf
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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
Handle: RePEc:fip:fedlwp:2013-010
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  1. Todd E. Clark & Michael W. McCracken, 2010. "Averaging forecasts from VARs with uncertain instabilities," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(1), pages 5-29.
  2. 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.
  3. 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.
  4. 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.
  5. Clark, Todd E. & West, Kenneth D., 2006. "Using out-of-sample mean squared prediction errors to test the martingale difference hypothesis," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 155-186.
  6. Berkowitz, Jeremy, 2001. "Testing Density Forecasts, with Applications to Risk Management," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(4), pages 465-474, October.
  7. Goncalves, Silvia & Kilian, Lutz, 2004. "Bootstrapping autoregressions with conditional heteroskedasticity of unknown form," Journal of Econometrics, Elsevier, vol. 123(1), pages 89-120, November.
  8. Mc Cracken, Michael W., 2000. "Robust out-of-sample inference," Journal of Econometrics, Elsevier, vol. 99(2), pages 195-223, December.
  9. 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.
  10. Andrea Carriero & Todd E. Clark & Massimiliano Marcellino, 2015. "Bayesian VARs: Specification Choices and Forecast Accuracy," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 30(1), pages 46-73, 01.
  11. Kenneth Beauchemin & Saeed Zaman, 2011. "A medium scale forecasting model for monetary policy," Working Paper 1128, Federal Reserve Bank of Cleveland.
  12. Kadiyala, K Rao & Karlsson, Sune, 1997. "Numerical Methods for Estimation and Inference in Bayesian VAR-Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 12(2), pages 99-132, March-Apr.
  13. Don Coletti & Stephen Murchison, 2002. "Models in Policy-Making," Bank of Canada Review, Bank of Canada, vol. 2002(Spring), pages 19-26.
  14. McCracken, Michael W., 2007. "Asymptotics for out of sample tests of Granger causality," Journal of Econometrics, Elsevier, vol. 140(2), pages 719-752, October.
  15. Clark, Todd E. & McCracken, Michael W., 2009. "Tests of Equal Predictive Ability With Real-Time Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 27(4), pages 441-454.
  16. Domenico Giannone & Michele Lenza & Giorgio E. Primiceri, 2015. "Prior Selection for Vector Autoregressions," The Review of Economics and Statistics, MIT Press, vol. 97(2), pages 436-451, May.
  17. Amisano, Gianni & Giacomini, Raffaella, 2007. "Comparing Density Forecasts via Weighted Likelihood Ratio Tests," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 177-190, April.
  18. 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.
  19. Schorfheide, Frank, 2005. "VAR forecasting under misspecification," Journal of Econometrics, Elsevier, vol. 128(1), pages 99-136, September.
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