IDEAS home Printed from
MyIDEAS: Log in (now much improved!) to save this article

Combining Forecasts from Nested Models

  • Todd E. Clark
  • Michael W. McCracken

Motivated by the common finding that linear autoregressive models often forecast better than models that incorporate additional information, this paper presents analytical, Monte Carlo and empirical evidence on the effectiveness of combining forecasts from nested models. In our analytics, the unrestricted model is true, but a subset of the coefficients is treated as being local-to-zero. This approach captures the practical reality that the predictive content of variables of interest is often low. We derive mean square error-minimizing weights for combining the restricted and unrestricted forecasts. Monte Carlo and empirical analyses verify the practical effectiveness of our combination approach. Copyright (c) Blackwell Publishing Ltd and the Department of Economics, University of Oxford, 2009.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL:
File Function: link to full text
Download Restriction: Access to full text is restricted to subscribers.

As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

Article provided by Department of Economics, University of Oxford in its journal Oxford Bulletin of Economics and Statistics.

Volume (Year): 71 (2009)
Issue (Month): 3 (06)
Pages: 303-329

in new window

Handle: RePEc:bla:obuest:v:71:y:2009:i:3:p:303-329
Contact details of provider: Postal:
Manor Rd. Building, Oxford, OX1 3UQ

Web page:

More information through EDIRC

Order Information: Web:

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

as in new window
  1. Bossaerts, Peter & Hillion, Pierre, 1999. "Implementing Statistical Criteria to Select Return Forecasting Models: What Do We Learn?," Review of Financial Studies, Society for Financial Studies, vol. 12(2), pages 405-28.
  2. Flint Brayton & John M. Roberts & John C. Williams, 1999. "What's happened to the Phillips curve?," Finance and Economics Discussion Series 1999-49, Board of Governors of the Federal Reserve System (U.S.).
  3. Hansen, Bruce E., 1992. "Convergence to Stochastic Integrals for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 8(04), pages 489-500, December.
  4. Richard Clarida & Lucio Sarno & Mark Taylor & Giorgio Valente, 2001. "The Out-of-Sample Success of Term Structure Models as Exchange Rate Predictors: A Step Beyond," NBER Working Papers 8601, National Bureau of Economic Research, Inc.
  5. David Hendry & Michael P. Clements, 2001. "Pooling of Forecasts," Economics Papers 2002-W9, Economics Group, Nuffield College, University of Oxford.
  6. Jean Boivin & Serena Ng, 2005. "Understanding and Comparing Factor-Based Forecasts," NBER Working Papers 11285, National Bureau of Economic Research, Inc.
  7. Ben S. Bernanke & Jean Boivin, 2001. "Monetary Policy in a Data-Rich Environment," NBER Working Papers 8379, National Bureau of Economic Research, Inc.
  8. 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, 06.
  9. Davidson, James & de Jong, Robert M., 2000. "The Functional Central Limit Theorem And Weak Convergence To Stochastic Integrals Ii," Econometric Theory, Cambridge University Press, vol. 16(05), pages 643-666, October.
  10. Massimiliano Marcellino & James Stock & Mark Watson, 2005. "A Comparison of Direct and Iterated Multistep AR Methods for Forecasting Macroeconomic Time Series," Working Papers 285, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
  11. Clark, Todd E. & West, Kenneth D., 2007. "Approximately normal tests for equal predictive accuracy in nested models," Journal of Econometrics, Elsevier, vol. 138(1), pages 291-311, May.
  12. Athanasios Orphanides & Simon van Norden, 2003. "The Reliability of Inflation Forecasts Based on Output Gap Estimates in Real Time," CIRANO Working Papers 2003s-01, CIRANO.
  13. Andrew Atkeson & Lee E. Ohanian, 2001. "Are Phillips curves useful for forecasting inflation?," Quarterly Review, Federal Reserve Bank of Minneapolis, issue Win, pages 2-11.
  14. Todd Clark & Michael McCracken, 2005. "Evaluating Direct Multistep Forecasts," Econometric Reviews, Taylor & Francis Journals, vol. 24(4), pages 369-404.
  15. James H. Stock & Mark W.Watson, 2003. "Forecasting Output and Inflation: The Role of Asset Prices," Journal of Economic Literature, American Economic Association, vol. 41(3), pages 788-829, September.
  16. Litterman, Robert B, 1986. "Forecasting with Bayesian Vector Autoregressions-Five Years of Experience," Journal of Business & Economic Statistics, American Statistical Association, vol. 4(1), pages 25-38, January.
  17. Arulampalam, W. & Robin A. Naylor & Jeremy P. Smith, 2002. "University of Warwick," Royal Economic Society Annual Conference 2002 9, Royal Economic Society.
  18. Michael W. McCracken & Todd E. Clark, 2003. "The Predictive Content of the Output Gap for Inflation: Resolving In-Sample and Out-of-Sample Evidence," Computing in Economics and Finance 2003 183, Society for Computational Economics.
  19. Stephen G. Cecchetti, 1995. "Inflation Indicators and Inflation Policy," NBER Chapters, in: NBER Macroeconomics Annual 1995, Volume 10, pages 189-236 National Bureau of Economic Research, Inc.
  20. Gary Koop & Simon Potter, 2004. "Forecasting in dynamic factor models using Bayesian model averaging," Econometrics Journal, Royal Economic Society, vol. 7(2), pages 550-565, December.
  21. Clements,Michael & Hendry,David, 1998. "Forecasting Economic Time Series," Cambridge Books, Cambridge University Press, number 9780521632423, November.
  22. John Y. Campbell & Samuel B. Thompson, 2005. "Predicting the Equity Premium Out of Sample: Can Anything Beat the Historical Average?," NBER Working Papers 11468, National Bureau of Economic Research, Inc.
  23. Todd E. Clark & Michael W. McCracken, 1999. "Tests of equal forecast accuracy and encompassing for nested models," Research Working Paper 99-11, Federal Reserve Bank of Kansas City.
  24. Rotemberg, Julio J & Woodford, Michael, 1996. "Real-Business-Cycle Models and the Forecastable Movements in Output, Hours, and Consumption," American Economic Review, American Economic Association, vol. 86(1), pages 71-89, March.
  25. Pesaran, M. Hashem & Timmermann, Allan, 2002. "Market timing and return prediction under model instability," Journal of Empirical Finance, Elsevier, vol. 9(5), pages 495-510, December.
  26. James H. Stock & Mark W. Watson, 1994. "Evidence on Structural Instability in Macroeconomic Time Series Relations," NBER Technical Working Papers 0164, National Bureau of Economic Research, Inc.
  27. James H. Stock & Mark W. Watson, 1999. "Forecasting Inflation," NBER Working Papers 7023, National Bureau of Economic Research, Inc.
  28. 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.
  29. Richard H. Clarida & Mark P. Taylor, 1997. "The Term Structure Of Forward Exchange Premiums And The Forecastability Of Spot Exchange Rates: Correcting The Errors," The Review of Economics and Statistics, MIT Press, vol. 79(3), pages 353-361, August.
  30. John C. Robertson & Ellis W. Tallman, 1999. "Vector autoregressions: forecasting and reality," Economic Review, Federal Reserve Bank of Atlanta, issue Q1, pages 4-18.
  31. Thomas Doan & Robert B. Litterman & Christopher A. Sims, 1983. "Forecasting and Conditional Projection Using Realistic Prior Distributions," NBER Working Papers 1202, National Bureau of Economic Research, Inc.
  32. Elliott, Graham & Timmermann, Allan, 2002. "Optimal Forecast Combination Under General Loss Functions and Forecast Error Distributions," University of California at San Diego, Economics Working Paper Series qt15r9t2q2, Department of Economics, UC San Diego.
  33. 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.
  34. McCracken, Michael W., 2007. "Asymptotics for out of sample tests of Granger causality," Journal of Econometrics, Elsevier, vol. 140(2), pages 719-752, October.
  35. Robert J. Gordon, 1998. "Foundations of the Goldilocks Economy: Supply Shocks and the Time-Varying NAIRU," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 29(2), pages 297-346.
  36. Mototsugu Shintani, 2003. "Nonlinear Forecasting Analysis Using Diffusion Indexes: An Application to Japan," Vanderbilt University Department of Economics Working Papers 0322, Vanderbilt University Department of Economics, revised Apr 2004.
  37. Stock, James H & Watson, Mark W, 2002. "Macroeconomic Forecasting Using Diffusion Indexes," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(2), pages 147-62, April.
  38. Carmen Fernández & Eduardo Ley & Mark F. J. Steel, . "Benchmark priors for Bayesian Model averaging," Working Papers 98-06, FEDEA.
  39. Jonas D. M. Fisher & Chin Te Liu & Ruilin Zhou, 2002. "When can we forecast inflation?," Economic Perspectives, Federal Reserve Bank of Chicago, issue Q I, pages 32-44.
  40. Amit Goyal & Ivo Welch, 2002. "Predicting the Equity Premium With Dividend Ratios," NBER Working Papers 8788, National Bureau of Economic Research, Inc.
  41. Scott Brave & Jonas D. M. Fisher, 2004. "In search of a robust inflation forecast," Economic Perspectives, Federal Reserve Bank of Chicago, issue Q IV, pages 12-31.
  42. repec:cup:etheor:v:8:y:1992:i:4:p:489-500 is not listed on IDEAS
  43. Inoue, Atsushi & Kilian, Lutz, 2003. "On the Selection of Forecasting Models," CEPR Discussion Papers 3809, C.E.P.R. Discussion Papers.
  44. William T. Gavin & Kevin L. Kliesen, 2002. "Unemployment insurance claims and economic activity," Review, Federal Reserve Bank of St. Louis, issue May, pages 15-28.
  45. Rotemberg, Julio J., 1996. "Prices, output, and hours: An empirical analysis based on a sticky price model," Journal of Monetary Economics, Elsevier, vol. 37(3), pages 505-533, June.
  46. Godfrey, Leslie G. & Orme, Chris D., 2004. "Controlling the finite sample significance levels of heteroskedasticity-robust tests of several linear restrictions on regression coefficients," Economics Letters, Elsevier, vol. 82(2), pages 281-287, February.
  47. Yash P. Mehra, 1990. "Real output and unit labor costs as predictors of inflation," Economic Review, Federal Reserve Bank of Richmond, issue Jul, pages 31-39.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:bla:obuest:v:71:y:2009:i:3:p:303-329. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Wiley-Blackwell Digital Licensing)

or (Christopher F. Baum)

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.