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Revisiting useful approaches to data-rich macroeconomic forecasting

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Jan J. J. Groen
George Kapetanios

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Abstract

This paper revisits a number of data-rich prediction methods that are widely used in macroeconomic forecasting, such as factor models and Bayesian shrinkage regression, and compares these methods with a lesser known alternative: partial least squares regression. In this method, linear, orthogonal combinations of a large number of predictor variables are constructed such that the linear combinations maximize the covariance between the target variable and each of the common components constructed from the predictor variables. We provide a theorem that shows that when the data comply with a factor structure, principal components and partial least squares regressions provide asymptotically similar results. We also argue that forecast combinations can be interpreted as a restricted form of partial least squares regression. Monte Carlo experiments confirm our theoretical results that partial least squares regression performs at least as well as principal components regression and rivals Bayesian regression when the data have a factor structure. These experiments also indicate that when there is no factor structure in the data, partial least square regression outperforms both principal components and Bayesian regressions. Finally, we apply partial least squares, principal components, and Bayesian regressions on a large panel of monthly U.S. macroeconomic and financial data to forecast CPI inflation, core CPI inflation, industrial production, unemployment, and the federal funds rate across different subperiods. The results indicate that partial least squares regression usually has the best out-of-sample performance when compared with the two other data-rich prediction methods.

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Paper provided by Federal Reserve Bank of New York in its series Staff Reports with number 327.

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Date of creation: 2008
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Handle: RePEc:fip:fednsr:327

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Keywords: Time-series analysis ; Economic forecasting ; Business cycles ; Econometric models;

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  6. 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. [Downloadable!] (restricted)
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  9. Jon Faust & Jonathan H. Wright, 2007. "Comparing Greenbook and Reduced Form Forecasts using a Large Realtime Dataset," NBER Working Papers 13397, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  10. 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. [Downloadable!] (restricted)
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  11. Christine De Mol & Domenico Giannone & Lucrezia Reichlin, 2006. "Forecasting using a large number of predictors - Is Bayesian regression a valid alternative to principal components?," Working Paper Series 700, European Central Bank. [Downloadable!]
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  12. Marianne Sensier & Dick van Dijk, 2004. "Testing for Volatility Changes in U.S. Macroeconomic Time Series," The Review of Economics and Statistics, MIT Press, vol. 86(3), pages 833-839, 08. [Downloadable!] (restricted)
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  13. Richard Clarida & Jordi Galí & Mark Gertler, 2000. "Monetary Policy Rules And Macroeconomic Stability: Evidence And Some Theory," The Quarterly Journal of Economics, MIT Press, vol. 115(1), pages 147-180, February. [Downloadable!] (restricted)
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  14. 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. [Downloadable!] (restricted)
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  15. George Kapetanios & Massimiliano Marcellino, 2003. "A Comparison of Estimation Methods for Dynamic Factor Models of Large Dimensions," Working Papers 489, Queen Mary, University of London, Department of Economics. [Downloadable!]
  16. Timmermann, Allan, 2006. "Forecast Combinations," Handbook of Economic Forecasting, Elsevier. [Downloadable!] (restricted)
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  19. Antonello D'Agostino & Domenico Giannone, 2006. "Comparing alternative predictors based on large-panel factor models," Working Paper Series 680, European Central Bank. [Downloadable!]
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