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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. Andrea Carriero & Todd Clark & Massimiliano Marcellino, 2011. "Bayesian VARs: specification choices and forecast accuracy," Working Paper 1112, Federal Reserve Bank of Cleveland.
  2. 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.
  3. Kenneth Beauchemin & Saeed Zaman, 2011. "A medium scale forecasting model for monetary policy," Working Paper 1128, Federal Reserve Bank of Cleveland.
  4. Kilian, Lutz & Gonçalves, Sílvia, 2002. "Bootstrapping Autoregressions with Conditional Heteroskedasticity of Unknown Form," Discussion Paper Series 1: Economic Studies 2002,26, Deutsche Bundesbank, Research Centre.
  5. McCracken, Michael W., 2007. "Asymptotics for out of sample tests of Granger causality," Journal of Econometrics, Elsevier, vol. 140(2), pages 719-752, October.
  6. 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.
  7. 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.
  8. Kadiyala, K. Rao & Karlsson, Sune, 1994. "Numerical Aspects of Bayesian VAR-modeling," Working Paper Series in Economics and Finance 12, Stockholm School of Economics.
  9. 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.
  10. Giannone, Domenico & Lenza, Michele & Primiceri, Giorgio E., 2012. "Prior selection for vector autoregressions," Working Paper Series 1494, European Central Bank.
  11. Todd E. Clark & Michael W. McCracken, 2008. "Averaging forecasts from VARs with uncertain instabilities," Working Papers 2008-030, Federal Reserve Bank of St. Louis.
  12. 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.
  13. 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.
  14. Gianni Amisano & Raffaella Giacomini, 2005. "Comparing Density Forecsts via Weighted Likelihood Ratio Tests," Working Papers ubs0504, University of Brescia, Department of Economics.
  15. Mc Cracken, Michael W., 2000. "Robust out-of-sample inference," Journal of Econometrics, Elsevier, vol. 99(2), pages 195-223, December.
  16. Don Coletti & Stephen Murchison, 2002. "Models in Policy-Making," Bank of Canada Review, Bank of Canada, vol. 2002(Spring), pages 19-26.
  17. 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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