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Are Forecast Combinations Efficient?

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  • Pablo Pincheira

Abstract

It is well known that weighted averages of two competing forecasts may reduce Mean Squared Prediction Errors (MSPE) and may also introduce certain inefficiencies. In this paper we take an in-depth view of one particular type of inefficiency stemming from simple combination schemes. We identify testable conditions under which every linear convex combination of two forecasts displays this type of inefficiency. In particular, we show that the process of taking averages of forecasts may induce inefficiencies in the combination, even when the individual forecasts are efficient. Furthermore, we show that the so-called "optimal weighted average" traditionally presented in the literature may indeed be suboptimal. We propose a simple testable condition to detect if this traditional weighted factor is optimal in a broader sense. An optimal "recombination weight" is introduced. Finally, we illustrate our findings with simulations and an empirical application in the context of the combination of inflation forecasts.

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Bibliographic Info

Paper provided by Central Bank of Chile in its series Working Papers Central Bank of Chile with number 661.

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Date of creation: Jan 2012
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Handle: RePEc:chb:bcchwp:661

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References

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  1. Mauro Costantini & Robert M. Kunst, 2011. "Combining forecasts based on multiple encompassing tests in a macroeconomic core system," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 30(6), pages 579-596, September.
  2. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 20(1), pages 134-44, January.
  3. Carlos Capistrán & Allan Timmermann, 2008. "Forecast Combination With Entry and Exit of Experts," CREATES Research Papers 2008-55, School of Economics and Management, University of Aarhus.
  4. Jonathan H. Wright, 2003. "Bayesian Model Averaging and exchange rate forecasts," International Finance Discussion Papers, Board of Governors of the Federal Reserve System (U.S.) 779, Board of Governors of the Federal Reserve System (U.S.).
  5. Mark W. Watson & James H. Stock, 2004. "Combination forecasts of output growth in a seven-country data set," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 23(6), pages 405-430.
  6. Diebold, Francis X, 1988. "Serial Correlation and the Combination of Forecasts," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 6(1), pages 105-11, January.
  7. Clements, Michael P. & Harvey, David I., 2011. "Combining probability forecasts," International Journal of Forecasting, Elsevier, vol. 27(2), pages 208-223.
  8. Aiolfi, Marco & Timmermann, Allan, 2006. "Persistence in forecasting performance and conditional combination strategies," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 31-53.
  9. Graham Elliott & Allan Timmermann, 2008. "Economic Forecasting," Journal of Economic Literature, American Economic Association, vol. 46(1), pages 3-56, March.
  10. Harvey, David I & Leybourne, Stephen J & Newbold, Paul, 1998. "Tests for Forecast Encompassing," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 16(2), pages 254-59, April.
  11. Hansen, Bruce E., 2008. "Least-squares forecast averaging," Journal of Econometrics, Elsevier, vol. 146(2), pages 342-350, October.
  12. Pincheira, Pablo & García, Álvaro, 2012. "En busca de un buen marco de referencia predictivo para la inflación en Chile," El Trimestre Económico, Fondo de Cultura Económica, vol. 0(313), pages 85-123, enero-mar.
  13. Chong, Yock Y & Hendry, David F, 1986. "Econometric Evaluation of Linear Macro-Economic Models," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 53(4), pages 671-90, August.
  14. Poncela, Pilar & Rodríguez, Julio & Sánchez-Mangas, Rocío & Senra, Eva, 2011. "Forecast combination through dimension reduction techniques," International Journal of Forecasting, Elsevier, vol. 27(2), pages 224-237.
  15. Pablo Matias Pincheira Brown, 2013. "Shrinkage‐Based Tests of Predictability," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 32(4), pages 307-332, 07.
  16. repec:taf:jnlbes:v:30:y:2012:i:1:p:1-17 is not listed on IDEAS
  17. Halbert White, 2000. "A Reality Check for Data Snooping," Econometrica, Econometric Society, Econometric Society, vol. 68(5), pages 1097-1126, September.
  18. Kolassa, Stephan, 2011. "Combining exponential smoothing forecasts using Akaike weights," International Journal of Forecasting, Elsevier, vol. 27(2), pages 238-251.
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Cited by:
  1. Pablo Pincheira, 2012. "A Joint Test of Superior Predictive Ability for Chilean Inflation Forecasts," Journal Economía Chilena (The Chilean Economy), Central Bank of Chile, vol. 15(3), pages 04-39, December.
  2. Luis Felipe Céspedes C. & Jorge A. Fornero & Jordi Galí, 2011. "Non-Ricardian Aspects of Fiscal Policy in Chile," Journal Economía Chilena (The Chilean Economy), Central Bank of Chile, vol. 14(2), pages 79-107, August.
  3. Pablo Pincheira & Carlos A. Medel, 2012. "Forecasting Inflation with a Simple and Accurate Benchmark: a Cross-Country Analysis," Working Papers Central Bank of Chile, Central Bank of Chile 677, Central Bank of Chile.

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