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Forecast Combinations

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  • Timmermann, Allan

Abstract

Forecast combinations have frequently been found in empirical studies to produce better forecasts on average than methods based on the ex-ante best individual forecasting model. Moreover, simple combinations that ignore correlations between forecast errors often dominate more refined combination schemes aimed at estimating the theoretically optimal combination weights. In this paper we analyse theoretically the factors that determine the advantages from combining forecasts (for example, the degree of correlation between forecast errors and the relative size of the individual models? forecast error variances). Although the reasons for the success of simple combination schemes are poorly understood, we discuss several possibilities related to model misspecification, instability (non-stationarities) and estimation error in situations where the numbers of models is large relative to the available sample size. We discuss the role of combinations under asymmetric loss and consider combinations of point, interval and probability forecasts.

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  • Timmermann, Allan, 2005. "Forecast Combinations," CEPR Discussion Papers 5361, C.E.P.R. Discussion Papers.
    • Handle: RePEc:cpr:ceprdp:5361
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    1. Pesaran, M. Hashem & Timmermann, Allan, 2005. "Small sample properties of forecasts from autoregressive models under structural breaks," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 183-217.
    2. Figlewski, Stephen & Urich, Thomas, 1983. "Optimal Aggregation of Money Supply Forecasts: Accuracy, Profitability and Market Efficiency," Journal of Finance, American Finance Association, vol. 38(3), pages 695-710, June.
    3. Forni, Mario & Hallin, Marc & Lippi, Marco & Reichlin, Lucrezia, 2005. "The Generalized Dynamic Factor Model: One-Sided Estimation and Forecasting," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 830-840, September.
    4. Giacomini, Raffaella & Komunjer, Ivana, 2005. "Evaluation and Combination of Conditional Quantile Forecasts," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 416-431, October.
    5. Clements, Michael P. & Hendry, David F., 2006. "Forecasting with Breaks," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 12, pages 605-657, Elsevier.
    6. Palm, F. & Zellner, A., 1991. "To combine or not to combine? issues of combining forecasts," LIDAM Discussion Papers CORE 1991022, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. Timmermann, Allan & Patton, Andrew, 2003. "Properties of Optimal Forecasts," CEPR Discussion Papers 4037, C.E.P.R. Discussion Papers.
    8. Forni, Mario & Hallin, Marc & Lippi, Marco & Reichlin, Lucrezia, 2004. "The generalized dynamic factor model consistency and rates," Journal of Econometrics, Elsevier, vol. 119(2), pages 231-255, April.
    9. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
    10. Armstrong, J. Scott, 1989. "Combining forecasts: The end of the beginning or the beginning of the end?," International Journal of Forecasting, Elsevier, vol. 5(4), pages 585-588.
    11. Diebold, Francis X., 1989. "Forecast combination and encompassing: Reconciling two divergent literatures," International Journal of Forecasting, Elsevier, vol. 5(4), pages 589-592.
    12. Ghysels, Eric & Granger, Clive W J & Siklos, Pierre L, 1996. "Is Seasonal Adjustment a Linear or Nonlinear Data-Filtering Process?," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 374-386, July.
    13. Boivin, Jean & Ng, Serena, 2006. "Are more data always better for factor analysis?," Journal of Econometrics, Elsevier, vol. 132(1), pages 169-194, May.
    14. Makridakis, Spyros, 1989. "Why combining works?," International Journal of Forecasting, Elsevier, vol. 5(4), pages 601-603.
    15. repec:cup:etheor:v:13:y:1997:i:6:p:808-17 is not listed on IDEAS
    16. Granger, Clive W. J. & Jeon, Yongil, 2004. "Thick modeling," Economic Modelling, Elsevier, vol. 21(2), pages 323-343, March.
    17. Yock Y. Chong & David F. Hendry, 1986. "Econometric Evaluation of Linear Macro-Economic Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(4), pages 671-690.
    18. Christoffersen, Peter F. & Diebold, Francis X., 1997. "Optimal Prediction Under Asymmetric Loss," Econometric Theory, Cambridge University Press, vol. 13(6), pages 808-817, December.
    19. Swanson, Norman R. & White, Halbert, 1997. "Forecasting economic time series using flexible versus fixed specification and linear versus nonlinear econometric models," International Journal of Forecasting, Elsevier, vol. 13(4), pages 439-461, December.
    20. Graham Elliott & Allan Timmermann, 2005. "Optimal Forecast Combination Under Regime Switching ," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 46(4), pages 1081-1102, November.
    21. Michael Artis & Anindya Banerjee & Massimiliano Marcellino, "undated". "Factor forecasts for the UK," Working Papers 203, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    22. Bunn, Derek W., 1985. "Statistical efficiency in the linear combination of forecasts," International Journal of Forecasting, Elsevier, vol. 1(2), pages 151-163.
    23. Timmermann, Allan, 2006. "Forecast Combinations," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 4, pages 135-196, Elsevier.
    24. Diebold, Francis X, 1988. "Serial Correlation and the Combination of Forecasts," Journal of Business & Economic Statistics, American Statistical Association, vol. 6(1), pages 105-111, January.
    25. Marco Aiolfi & Carlo Ambrogio Favero, "undated". "Model Uncertainty, Thick Modelling and the predictability of Stock Returns," Working Papers 221, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    26. Clemen, Robert T. & Murphy, Allan H. & Winkler, Robert L., 1995. "Screening probability forecasts: contrasts between choosing and combining," International Journal of Forecasting, Elsevier, vol. 11(1), pages 133-145, March.
    27. Findley, David F, 1996. "Is Seasonal Adjustment a Linear or Nonlinear Data-Filtering Process? Comment," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 389-393, July.
    28. Clements,Michael & Hendry,David, 1998. "Forecasting Economic Time Series," Cambridge Books, Cambridge University Press, number 9780521632423, October.
    29. LeSage, James P & Magura, Michael, 1992. "A Mixture-Model Approach to Combining Forecasts," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(4), pages 445-452, October.
    30. Capistrán, Carlos & Timmermann, Allan, 2009. "Forecast Combination With Entry and Exit of Experts," Journal of Business & Economic Statistics, American Statistical Association, vol. 27(4), pages 428-440.
    31. Garratt, Anthony & Koop, Gary & Mise, Emi & Vahey, Shaun P., 2009. "Real-Time Prediction With U.K. Monetary Aggregates in the Presence of Model Uncertainty," Journal of Business & Economic Statistics, American Statistical Association, vol. 27(4), pages 480-491.
    32. Elliott, Graham & Timmermann, Allan, 2004. "Optimal forecast combinations under general loss functions and forecast error distributions," Journal of Econometrics, Elsevier, vol. 122(1), pages 47-79, September.
    33. Ang, Andrew & Bekaert, Geert & Wei, Min, 2007. "Do macro variables, asset markets, or surveys forecast inflation better?," Journal of Monetary Economics, Elsevier, vol. 54(4), pages 1163-1212, May.
    34. Deutsch, Melinda & Granger, Clive W. J. & Terasvirta, Timo, 1994. "The combination of forecasts using changing weights," International Journal of Forecasting, Elsevier, vol. 10(1), pages 47-57, June.
    35. Hylleberg, Svend, 1996. "Is Seasonal Adjustment a Linear or Nonlinear Data-Filtering Process? Comment," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 388-389, July.
    36. Robert T. Clemen, 1987. "Combining Overlapping Information," Management Science, INFORMS, vol. 33(3), pages 373-380, March.
    37. Sune Karlsson & Tor Jacobson, 2004. "Finding good predictors for inflation: a Bayesian model averaging approach," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 23(7), pages 479-496.
    38. Mario Forni & Marc Hallin & Marco Lippi & Lucrezia Reichlin, 2000. "The Generalized Dynamic-Factor Model: Identification And Estimation," The Review of Economics and Statistics, MIT Press, vol. 82(4), pages 540-554, November.
    39. Clemon, Robert T & Winkler, Robert L, 1986. "Combining Economic Forecasts," Journal of Business & Economic Statistics, American Statistical Association, vol. 4(1), pages 39-46, January.
    40. Ledoit, Olivier & Wolf, Michael, 2003. "Improved estimation of the covariance matrix of stock returns with an application to portfolio selection," Journal of Empirical Finance, Elsevier, vol. 10(5), pages 603-621, December.
    41. Granger, Clive W.J. & Machina, Mark J., 2006. "Forecasting and Decision Theory," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 2, pages 81-98, Elsevier.
    42. Swanson, Norman R & Zeng, Tian, 2001. "Choosing among Competing Econometric Forecasts: Regression-Based Forecast Combination Using Model Selection," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 20(6), pages 425-440, September.
    43. Makridakis, Spyros & Hibon, Michele, 2000. "The M3-Competition: results, conclusions and implications," International Journal of Forecasting, Elsevier, vol. 16(4), pages 451-476.
    44. Corradi, Valentina & Fernandez, Andres & Swanson, Norman R., 2009. "Information in the Revision Process of Real-Time Datasets," Journal of Business & Economic Statistics, American Statistical Association, vol. 27(4), pages 455-467.
    45. Ghysels, Eric & Granger, Clive W J & Siklos, Pierre L, 1996. "Is Seasonal Adjustment a Linear or Nonlinear Data-Filtering Process? Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 396-397, July.
    46. Min, Chung-ki & Zellner, Arnold, 1993. "Bayesian and non-Bayesian methods for combining models and forecasts with applications to forecasting international growth rates," Journal of Econometrics, Elsevier, vol. 56(1-2), pages 89-118, March.
    47. Robert L. Winkler, 1981. "Combining Probability Distributions from Dependent Information Sources," Management Science, INFORMS, vol. 27(4), pages 479-488, April.
    48. Clemen, Robert T., 1989. "Combining forecasts: A review and annotated bibliography," International Journal of Forecasting, Elsevier, vol. 5(4), pages 559-583.
    49. Zellner, Arnold & Hong, Chansik & Min, Chung-ki, 1991. "Forecasting turning points in international output growth rates using Bayesian exponentially weighted autoregression, time-varying parameter, and pooling techniques," Journal of Econometrics, Elsevier, vol. 49(1-2), pages 275-304.
    50. Michael P. Clements & David I. Harvey, 2010. "Forecast encompassing tests and probability forecasts," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(6), pages 1028-1062.
    51. Spyros Makridakis & Robert L. Winkler, 1983. "Averages of Forecasts: Some Empirical Results," Management Science, INFORMS, vol. 29(9), pages 987-996, September.
    52. Francis X. Diebold & Jose A. Lopez, 1995. "Forecast evaluation and combination," Research Paper 9525, Federal Reserve Bank of New York.
    53. Watson, Mark W, 1996. "Is Seasonal Adjustment a Linear or Nonlinear Data-Filtering Process? Comment," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 394-396, July.
    54. Stock, James H & Watson, Mark W, 1996. "Evidence on Structural Instability in Macroeconomic Time Series Relations," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(1), pages 11-30, January.
    55. Stock, James H & Watson, Mark W, 2002. "Macroeconomic Forecasting Using Diffusion Indexes," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(2), pages 147-162, April.
    56. Terasvirta, Timo, 2006. "Forecasting economic variables with nonlinear models," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 8, pages 413-457, Elsevier.
    57. David F. Hendry & Michael P. Clements, 2004. "Pooling of forecasts," Econometrics Journal, Royal Economic Society, vol. 7(1), pages 1-31, June.
    58. Yeung Lewis Chan & James H. Stock & Mark W. Watson, 1999. "A dynamic factor model framework for forecast combination," Spanish Economic Review, Springer;Spanish Economic Association, vol. 1(2), pages 91-121.
    59. Diebold, Francis X. & Pauly, Peter, 1990. "The use of prior information in forecast combination," International Journal of Forecasting, Elsevier, vol. 6(4), pages 503-508, December.
    60. Engle, Robert F. & Granger, C. W. J. & Kraft, Dennis, 1984. "Combining competing forecasts of inflation using a bivariate arch model," Journal of Economic Dynamics and Control, Elsevier, vol. 8(2), pages 151-165, November.
    61. Aiolfi, Marco & Timmermann, Allan, 2006. "Persistence in forecasting performance and conditional combination strategies," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 31-53.
    62. Pesaran, M. Hashem & Timmermann, Allan, 2007. "Selection of estimation window in the presence of breaks," Journal of Econometrics, Elsevier, vol. 137(1), pages 134-161, March.
    63. Massimiliano Marcellino, "undated". "Forecast pooling for short time series of macroeconomic variables," Working Papers 212, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    64. repec:bla:jfinan:v:58:y:2003:i:4:p:1651-1684 is not listed on IDEAS
    65. Jeremy Smith & Kenneth F. Wallis, 2009. "A Simple Explanation of the Forecast Combination Puzzle," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 71(3), pages 331-355, June.
    66. Sunil Gupta & Peter C. Wilton, 1987. "Combination of Forecasts: An Extension," Management Science, INFORMS, vol. 33(3), pages 356-372, March.
    67. G. Elliott & C. Granger & A. Timmermann (ed.), 2006. "Handbook of Economic Forecasting," Handbook of Economic Forecasting, Elsevier, edition 1, volume 1, number 1.
    68. Heejoon Kang, 1986. "Unstable Weights in the Combination of Forecasts," Management Science, INFORMS, vol. 32(6), pages 683-695, June.
    69. 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.
    70. Winkler, Robert L., 1989. "Combining forecasts: A philosophical basis and some current issues," International Journal of Forecasting, Elsevier, vol. 5(4), pages 605-609.
    71. Bell, William R, 1996. "Is Seasonal Adjustment a Linear or Nonlinear Data-Filtering Process? Comment," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 387-388, July.
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    Keywords

    Forecast combinations; Pooling and trimming; Shrinkage methods; Model misspecification; Diversification gains;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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