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Forecasting with Factor-Augmented Regression: A Frequentist Model Averaging Approach

  • Xu Cheng

    ()

    (Department of Economics, University of Pennsylvania)

  • Bruce E. Hansen

    ()

    (Department of Economics, University of Wisconsin-Madison)

This paper considers forecast combination with factor-augmented regression. In this framework, a large number of forecasting models are available, varying by the choice of factors and the number of lags. We investigate forecast combination using weights that minimize the Mallows and the leave-h-out cross validation criteria. The unobserved factor regressors are estimated by principle components of a large panel with N predictors over T periods. With these generated regressors, we show that the Mallows and leave-h-out cross validation criteria are approximately unbiased estimators of the one-step-ahead and multi-step-ahead mean squared forecast errors, respectively, provided that N, T —› ∞. In contrast to well-known results in the literature, the generated-regressor issue can be ignored for forecast combination, without restrictions on the relation between N and T. Simulations show that the Mallows model averaging and leave-h-out cross-validation averaging methods yield lower mean squared forecast errors than alternative model selection and averaging methods such as AIC, BIC, cross validation, and Bayesian model averaging. We apply the proposed methods to the U.S. macroeconomic data set in Stock and Watson (2012) and find that they compare favorably to many popular shrinkage-type forecasting methods.

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Paper provided by Penn Institute for Economic Research, Department of Economics, University of Pennsylvania in its series PIER Working Paper Archive with number 12-046.

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Length: 28 pages
Date of creation: 01 Oct 2012
Date of revision:
Handle: RePEc:pen:papers:12-046
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  1. Doz, Catherine & Giannone, Domenico & Reichlin, Lucrezia, 2006. "A quasi maximum likelihood approach for large approximate dynamic factor models," Working Paper Series 0674, European Central Bank.
  2. Andrews, Donald W. K., 1991. "Asymptotic optimality of generalized CL, cross-validation, and generalized cross-validation in regression with heteroskedastic errors," Journal of Econometrics, Elsevier, vol. 47(2-3), pages 359-377, February.
  3. ., 2013. "Eartheconomic Demand and Supply," Chapters, in: Earth Economics, chapter 8, pages 85-100 Edward Elgar Publishing.
  4. Jonathan H. Wright, 2003. "Forecasting U.S. inflation by Bayesian Model Averaging," International Finance Discussion Papers 780, Board of Governors of the Federal Reserve System (U.S.).
  5. Gonçalves, Sílvia & Perron, Benoit, 2014. "Bootstrapping factor-augmented regression models," Journal of Econometrics, Elsevier, vol. 182(1), pages 156-173.
  6. Geweke, John & Amisano, Gianni, 2011. "Optimal prediction pools," Journal of Econometrics, Elsevier, vol. 164(1), pages 130-141, September.
  7. Jean Boivin & Serena Ng, 2003. "Are More Data Always Better for Factor Analysis?," NBER Working Papers 9829, National Bureau of Economic Research, Inc.
  8. Pagan, Adrian, 1984. "Econometric Issues in the Analysis of Regressions with Generated Regressors," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 25(1), pages 221-47, February.
  9. Schorfheide, Frank, 2005. "VAR forecasting under misspecification," Journal of Econometrics, Elsevier, vol. 128(1), pages 99-136, September.
  10. Carmen Fernandez & Eduardo Ley & Mark Steel, 2001. "Model uncertainty in cross-country growth regressions," Econometrics 0110002, EconWPA.
  11. Jason M. Lindo & Jessamyn Schaller & Benjamin Hansen, 2013. "Economic Conditions and Child Abuse," NBER Working Papers 18994, National Bureau of Economic Research, Inc.
  12. Carmen Fernandez & Eduardo Ley & Mark F J Steel, 1998. "Benchmark priors for Bayesian model averaging," ESE Discussion Papers 26, Edinburgh School of Economics, University of Edinburgh.
  13. Mario Forni & Marc Hallin & Marco Lippi & Lucrezia Reichlin, 2003. "The Generalized Dynamic Factor Model. One-Sided Estimation and Forecasting," LEM Papers Series 2003/13, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
  14. ., 2013. "Islamic economics: state of the art," Chapters, in: What is Wrong with Islamic Economics?, chapter 1, pages 3-25 Edward Elgar Publishing.
  15. Choi, In, 2012. "Efficient Estimation Of Factor Models," Econometric Theory, Cambridge University Press, vol. 28(02), pages 274-308, April.
  16. James H. Stock & Mark W. Watson, 2005. "Implications of Dynamic Factor Models for VAR Analysis," NBER Working Papers 11467, National Bureau of Economic Research, Inc.
  17. Kim, Hyun Hak & Swanson, Norman R., 2014. "Forecasting financial and macroeconomic variables using data reduction methods: New empirical evidence," Journal of Econometrics, Elsevier, vol. 178(P2), pages 352-367.
  18. 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.
  19. Hansen, Bruce E., 2008. "Least-squares forecast averaging," Journal of Econometrics, Elsevier, vol. 146(2), pages 342-350, October.
  20. Hansen, Bruce E. & Racine, Jeffrey S., 2012. "Jackknife model averaging," Journal of Econometrics, Elsevier, vol. 167(1), pages 38-46.
  21. ., 2013. "The world economy at large," Chapters, in: Capitalism and Democracy, chapter 7, pages 137-160 Edward Elgar Publishing.
  22. Connor, Gregory & Korajczyk, Robert A, 1993. " A Test for the Number of Factors in an Approximate Factor Model," Journal of Finance, American Finance Association, vol. 48(4), pages 1263-91, September.
  23. ., 2013. "Regional economic development and competitiveness," Chapters, in: Regional Competitiveness and Smart Specialization in Europe, chapter 3, pages 33-53 Edward Elgar Publishing.
  24. Wright, Jonathan H., 2008. "Bayesian Model Averaging and exchange rate forecasts," Journal of Econometrics, Elsevier, vol. 146(2), pages 329-341, October.
  25. Xavier Sala-I-Martin & Gernot Doppelhofer & Ronald I. Miller, 2004. "Determinants of Long-Term Growth: A Bayesian Averaging of Classical Estimates (BACE) Approach," American Economic Review, American Economic Association, vol. 94(4), pages 813-835, September.
  26. Stock, James H. & Watson, Mark W., 2006. "Forecasting with Many Predictors," Handbook of Economic Forecasting, Elsevier.
  27. Hansen, Lars Peter, 2013. "Uncertainty Outside and Inside Economic Models," Nobel Prize in Economics documents 2013-7, Nobel Prize Committee.
  28. 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.
  29. Bai, Jushan & Ng, Serena, 2008. "Forecasting economic time series using targeted predictors," Journal of Econometrics, Elsevier, vol. 146(2), pages 304-317, October.
  30. Jushan Bai & Serena Ng, 2000. "Determining the Number of Factors in Approximate Factor Models," Boston College Working Papers in Economics 440, Boston College Department of Economics.
  31. ., 2013. "Semiotics for cultural political economy," Chapters, in: Towards a Cultural Political Economy, chapter 3, pages 96-144 Edward Elgar Publishing.
  32. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
  33. 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.
  34. ., 2013. "What is Islamic economics?," Chapters, in: What is Wrong with Islamic Economics?, chapter 3, pages 40-53 Edward Elgar Publishing.
  35. ., 2013. "Teaching the history of economic thought," Chapters, in: Defending the History of Economic Thought, chapter 4, pages 72-104 Edward Elgar Publishing.
  36. Chamberlain, Gary & Rothschild, Michael, 1983. "Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets," Econometrica, Econometric Society, vol. 51(5), pages 1281-304, September.
  37. ., 2013. "Political stability and economic development," Chapters, in: The Political Economy of Iraq, chapter 5, pages 67-87 Edward Elgar Publishing.
  38. Marco Aiolfi & Carlos Capistrán & Allan Timmermann, 2010. "Forecast Combinations," Working Papers 2010-04, Banco de México.
  39. ., 2013. "The rapidly changing world economy," Chapters, in: Global Finance After the Crisis, chapter 1, pages 1-10 Edward Elgar Publishing.
  40. Leeb, Hannes & P tscher, Benedikt M., 2003. "The Finite-Sample Distribution Of Post-Model-Selection Estimators And Uniform Versus Nonuniform Approximations," Econometric Theory, Cambridge University Press, vol. 19(01), pages 100-142, February.
  41. Elliott, Graham & Gargano, Antonio & Timmermann, Allan, 2013. "Complete subset regressions," Journal of Econometrics, Elsevier, vol. 177(2), pages 357-373.
  42. ., 2013. "Expanding the frontiers of economics," Chapters, in: What is Wrong with Islamic Economics?, chapter 6, pages 85-101 Edward Elgar Publishing.
  43. Kunal Sen, 2012. "The political dynamics of economic growth," Brooks World Poverty Institute Working Paper Series esid-005-12, BWPI, The University of Manchester.
  44. ., 2013. "From Islamic theology to Islamic economics," Chapters, in: What is Wrong with Islamic Economics?, chapter 5, pages 72-84 Edward Elgar Publishing.
  45. ., 2013. "Application to institutional economics," Chapters, in: Change and Continuity at the World Bank, chapter 7, pages 84-95 Edward Elgar Publishing.
  46. ., 2013. "The dynamics of epistemic economic change," Chapters, in: Change and Continuity at the World Bank, chapter 4, pages 53-62 Edward Elgar Publishing.
  47. Inoue, Atsushi & Kilian, Lutz, 2008. "How Useful Is Bagging in Forecasting Economic Time Series? A Case Study of U.S. Consumer Price Inflation," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 511-522, June.
  48. Breitung, Jörg & Tenhofen, Jörn, 2011. "GLS Estimation of Dynamic Factor Models," Journal of the American Statistical Association, American Statistical Association, vol. 106(495), pages 1150-1166.
  49. Francis X. Diebold & Jose A. Lopez, 1995. "Forecast evaluation and combination," Research Paper 9525, Federal Reserve Bank of New York.
  50. Eells, Linda, 2013. "Minnesota Applied Economist 723, Fall 2013," Minnesota Applied Economist/Minnesota Agricultural Economist 156267, University of Minnesota, Department of Applied Economics.
  51. Pesaran, M. Hashem & Pick, Andreas & Timmermann, Allan, 2011. "Variable selection, estimation and inference for multi-period forecasting problems," Journal of Econometrics, Elsevier, vol. 164(1), pages 173-187, September.
  52. ., 2013. "Cultural turns and beyond in political economy," Chapters, in: Towards a Cultural Political Economy, chapter 2, pages 72-95 Edward Elgar Publishing.
  53. ., 2013. "The intangible economy," Chapters, in: Intellectual Property Rights and the Financing of Technological Innovation, chapter 2, pages 12-71 Edward Elgar Publishing.
  54. Jushan Bai & Serena Ng, 2009. "Boosting diffusion indices," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(4), pages 607-629.
  55. ., 2013. "Political economy revisited," Chapters, in: Capitalism and Democracy, chapter 2, pages 25-44 Edward Elgar Publishing.
  56. ., 2013. "The Islamic economy," Chapters, in: Islamic Finance, chapter 3, pages 29-60 Edward Elgar Publishing.
  57. Forni, Mario & Lippi, Marco, 2001. "The Generalized Dynamic Factor Model: Representation Theory," Econometric Theory, Cambridge University Press, vol. 17(06), pages 1113-1141, December.
  58. Jushan Bai & Serena Ng, 2006. "Confidence Intervals for Diffusion Index Forecasts and Inference for Factor-Augmented Regressions," Econometrica, Econometric Society, vol. 74(4), pages 1133-1150, 07.
  59. Leeb, Hannes & P tscher, Benedikt M., 2008. "Can One Estimate The Unconditional Distribution Of Post-Model-Selection Estimators?," Econometric Theory, Cambridge University Press, vol. 24(02), pages 338-376, April.
  60. ., 2013. "Why study the history of economic thought," Chapters, in: Defending the History of Economic Thought, chapter 2, pages 16-42 Edward Elgar Publishing.
  61. Avramov, Doron, 2002. "Stock return predictability and model uncertainty," Journal of Financial Economics, Elsevier, vol. 64(3), pages 423-458, June.
  62. ., 2013. "Methodology of Islamic economics," Chapters, in: What is Wrong with Islamic Economics?, chapter 4, pages 54-71 Edward Elgar Publishing.
  63. ., 2013. "Industrial economics," Chapters, in: Cartels, Competition and Public Procurement, chapter 3, pages 14-35 Edward Elgar Publishing.
  64. Chirok Han & Hyelim Lee, 2013. "Dependence Of Economic Growth On Co2 Emissions," Journal of Economic Development, Chung-Ang Unviersity, Department of Economics, vol. 38(1), pages 47-57, March.
  65. 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.
  66. ., 2013. "An Islamic economic system or spiritual capitalism?," Chapters, in: What is Wrong with Islamic Economics?, chapter 7, pages 102-120 Edward Elgar Publishing.
  67. Connor, Gregory & Korajczyk, Robert A., 1986. "Performance measurement with the arbitrage pricing theory : A new framework for analysis," Journal of Financial Economics, Elsevier, vol. 15(3), pages 373-394, March.
  68. Oecd, 2013. "The App Economy," OECD Digital Economy Papers 230, OECD Publishing.
  69. Bruce E. Hansen, 2007. "Least Squares Model Averaging," Econometrica, Econometric Society, vol. 75(4), pages 1175-1189, 07.
  70. ., 2013. "Limits of economic theories and concluding remarks," Chapters, in: Cartels, Competition and Public Procurement, chapter 11, pages 212-216 Edward Elgar Publishing.
  71. ., 2013. "Population and key macroeconomic variables," Chapters, in: The Political Economy of Iraq, chapter 2, pages 6-24 Edward Elgar Publishing.
  72. ., 2013. "Scientific issues in structural econometrics," Chapters, in: Rational Econometric Man, chapter 8, pages 251-290 Edward Elgar Publishing.
  73. Hjort N.L. & Claeskens G., 2003. "Frequentist Model Average Estimators," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 879-899, January.
  74. Clemen, Robert T., 1989. "Combining forecasts: A review and annotated bibliography," International Journal of Forecasting, Elsevier, vol. 5(4), pages 559-583.
  75. Hansen, Lars Peter & Hodrick, Robert J, 1980. "Forward Exchange Rates as Optimal Predictors of Future Spot Rates: An Econometric Analysis," Journal of Political Economy, University of Chicago Press, vol. 88(5), pages 829-53, October.
  76. Onatski, Alexei, 2012. "Asymptotics of the principal components estimator of large factor models with weakly influential factors," Journal of Econometrics, Elsevier, vol. 168(2), pages 244-258.
  77. Ben S. Bernanke & Jean Boivin & Piotr Eliasz, 2005. "Measuring the Effects of Monetary Policy: A Factor-Augmented Vector Autoregressive (FAVAR) Approach," The Quarterly Journal of Economics, Oxford University Press, vol. 120(1), pages 387-422.
  78. Lars Peter Hansen & Thomas J. Sargent, 2013. "Recursive Models of Dynamic Linear Economies," Economics Books, Princeton University Press, edition 1, number 10141.
  79. Stock J.H. & Watson M.W., 2002. "Forecasting Using Principal Components From a Large Number of Predictors," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1167-1179, December.
  80. James H. Stock & Mark W. Watson, 2012. "Generalized Shrinkage Methods for Forecasting Using Many Predictors," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(4), pages 481-493, June.
  81. ., 2013. "The ‘why’ of Islamic economics," Chapters, in: What is Wrong with Islamic Economics?, chapter 2, pages 26-39 Edward Elgar Publishing.
  82. ., 2013. "Government failure, IPRs and economic development," Chapters, in: Government Failure, chapter 7, pages 65-74 Edward Elgar Publishing.
  83. ., 2013. "Defending the history of economic thought," Chapters, in: Defending the History of Economic Thought, chapter 5, pages 105-132 Edward Elgar Publishing.
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