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Evaluating the accuracy of forecasts from vector autoregressions

  • 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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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
Date of revision:
Handle: RePEc:fip:fedlwp:2013-010
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  1. 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.
  2. Todd E. Clark & Michael W. McCracken, 2000. "Tests of Equal Forecast Accuracy and Encompassing for Nested Models," Econometric Society World Congress 2000 Contributed Papers 0319, Econometric Society.
  3. Todd E. Clark & Michael W. McCracken, 2006. "Averaging forecasts from VARs with uncertain instabilities," Research Working Paper RWP 06-12, Federal Reserve Bank of Kansas City.
  4. Gonçalves, Sílvia & Kilian, Lutz, 2002. "Bootstrapping autoregressions with conditional heteroskedasticity of unknown form," Working Paper Series 0196, European Central Bank.
  5. Schorfheide, Frank, 2005. "VAR forecasting under misspecification," Journal of Econometrics, Elsevier, vol. 128(1), pages 99-136, September.
  6. Kenneth D. West & Todd Clark, 2006. "Approximately Normal Tests for Equal Predictive Accuracy in Nested Models," NBER Technical Working Papers 0326, National Bureau of Economic Research, Inc.
  7. 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.
  8. McCracken, Michael W., 2007. "Asymptotics for out of sample tests of Granger causality," Journal of Econometrics, Elsevier, vol. 140(2), pages 719-752, October.
  9. Andrea Carriero & Todd E. Clark & Massimiliano Marcellino, 2011. "Bayesian VARs: specification choices and forecast accuracy," Working Paper 1112, Federal Reserve Bank of Cleveland.
  10. Don Coletti & Stephen Murchison, 2002. "Models in Policy-Making," Bank of Canada Review, Bank of Canada, vol. 2002(Spring), pages 19-26.
  11. Mc Cracken, Michael W., 2000. "Robust out-of-sample inference," Journal of Econometrics, Elsevier, vol. 99(2), pages 195-223, December.
  12. 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.
  13. 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.
  14. Hilde C. Bjørnland & Karsten Gerdrup & Anne Sofie Jore & Christie Smith & Leif Anders Thorsrud, 2009. "Does forecast combination improve Norges Bank inflation forecasts?," Working Paper 2009/01, Norges Bank.
  15. Kenneth Beauchemin & Saeed Zaman, 2011. "A medium scale forecasting model for monetary policy," Working Paper 1128, Federal Reserve Bank of Cleveland.
  16. 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.
  17. Todd E. Clark & Michael W. McCracken, 2007. "Tests of equal predictive ability with real-time data," Research Working Paper RWP 07-06, Federal Reserve Bank of Kansas City.
  18. Kadiyala, K. Rao & Karlsson, Sune, 1994. "Numerical Aspects of Bayesian VAR-modeling," SSE/EFI Working Paper Series in Economics and Finance 12, Stockholm School of Economics.
  19. 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.
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