Giovannelli, Alessandro and Proietti, Tommaso
(2014):
*On the Selection of Common Factors for Macroeconomic Forecasting.*

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## Abstract

We address the problem of selecting the common factors that are relevant for forecasting macroeconomic variables. In economic forecasting using diffusion indexes the factors are ordered, according to their importance, in terms of relative variability, and are the same for each variable to predict, i.e. the process of selecting the factors is not supervised by the predictand. We propose a simple and operational supervised method, based on selecting the factors on the basis of their significance in the regression of the predictand on the predictors. Given a potentially large number of predictors, we consider linear transformations obtained by principal components analysis. The orthogonality of the components implies that the standard t-statistics for the inclusion of a particular component are independent, and thus applying a selection procedure that takes into account the multiplicity of the hypotheses tests is both correct and computationally feasible. We focus on three main multiple testing procedures: Holm’s sequential method, controlling the family wise error rate, the Benjamini-Hochberg method, controlling the false discovery rate, and a procedure for incorporating prior information on the ordering of the components, based on weighting the p-values according to the eigenvalues associated to the components. We compare the empirical performances of these methods with the classical diffusion index (DI) approach proposed by Stock and Watson, conducting a pseudo-real time forecasting exercise, assessing the predictions of 8 macroeconomic variables using factors extracted from an U.S. dataset consisting of 121 quarterly time series. The overall conclusion is that nature is tricky, but essentially benign: the information that is relevant for prediction is effectively condensed by the first few factors. However, variable selection, leading to exclude some of the low order principal components, can lead to a sizable improvement in forecasting in specific cases. Only in one instance, real personal income, we were able to detect a significant contribution from high order components.

Item Type: | MPRA Paper |
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Original Title: | On the Selection of Common Factors for Macroeconomic Forecasting |

Language: | English |

Keywords: | Variable selection; Multiple testing; p-value weighting. |

Subjects: | C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C22 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables > C32 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes ; State Space Models C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables > C38 - Classification Methods ; Cluster Analysis ; Principal Components ; Factor Models C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C53 - Forecasting and Prediction Methods ; Simulation Methods E - Macroeconomics and Monetary Economics > E3 - Prices, Business Fluctuations, and Cycles E - Macroeconomics and Monetary Economics > E3 - Prices, Business Fluctuations, and Cycles > E32 - Business Fluctuations ; Cycles |

Item ID: | 60673 |

Depositing User: | Tommaso Proietti |

Date Deposited: | 16 Dec 2014 14:22 |

Last Modified: | 28 Sep 2019 01:04 |

References: | Bai, J. and Ng, S. (2002). “Determining the Number of Factors in Approximate Factor Models.” Econometrica, 70(1):191–221. Bai, J. and Ng, S. (2006). “Confidence Intervals for Diffusion Index Forecasts and Inference with Factor-Augmented Regressions.” Econometrica, 4(4):1133–1150. Bai, J. and Ng, S. (2008). “Forecasting Economic Time Series Using Targeted Predictors.” Journal of Econometrics, 146(2):304–317. Bai, J. and Ng, S. (2009). “Boosting Diffusion Indices.” Journal of Applied Econometrics, 24(4):607–629. Bair, E., Hastie, T., Debashis, P., and Tibshirani, R. (2006). “Prediction by Supervised Principal Components.” Journal of the American Statistical Association, 101(473):119–137. Benjamini, Y. and Hochberg, Y. (1995). “Controlling the False Discovery Rate: a Practical and Powerful Approach to Multiple Testing.” Journal of the Royal Statistical Society. Series B (Methodological), 289–300. Breitung, J. and Eickmeier, S. (2006). “Dynamic Factor Models.” In Modern Econometric Analysis, 25–40. Springer. Chun, H. and Keles¸, S. (2010). “Sparse Partial Least Squares Regression for Simultaneous Dimension Reduction and Variable Selection.” Journal of the Royal Statistical Society: Series B (Statistical Methodology), 72(1):3–25. Cook, R. D. (2007). “Fisher lecture: Dimension Reduction in Regression.” Statistical Science, 1–26. Cook, R. D. and Forzani, L. (2008). “Principal Fitted Components for Dimension Reduction in Regression.” Statistical Science, 52:485–501. Cox, D. (1968). “Notes on Some Aspects of Regression Analysis.” Journal of the Royal Statistical Society, Series A, 131(3):265–279. D’Agostino, A. and Giannone, D. (2012). “Comparing Alternative Predictors Based on Large-Panel Factor Models.” Oxford Bulletin of Economics and Statistics, 74(2):306–326. De Mol, C., Giannone, D., and Reichlin, L. (2008). "Forecasting Using a Large Number of Predictors: Is Bayesian Shrinkage a Valid Alternative to Principal omponents?” Journal of Econometrics, 146(2):318–328. Efron, B. (2010). Large-Scale Inference: Empirical Bayes Methods for Estimation, Testing, and Prediction. Institute of Mathematical Statistics Monographs. Cambridge University Press. Fan, J., Guo, S., and Hao, N. (2012). “Variance Estimation Using Refitted Cross-Validation in Ultrahigh Dimensional Regression.” Journal of the Royal Statistical Society: Series B (Statistical Methodology), 74(1):37–65. Forni, M., Hallin, M., Lippi, M., and Reichlin, L. (2005). “The Generalized Dynamic Factor Model: One-Sided Estimation and Forecasting.” Journal of the American Statistical Association, 100:830–840. Fuentes, J., Poncela, P., and Rodrıguez, J. (2014). “Sparse Partial Least Squares in Time Series for Macroeconomic Forecasting.” Journal of Applied Econometrics. Genovese, C. R., Roeder, K., and Wasserman, L. (2006). “False Discovery Control with p-value Weighting.” Biometrika, 93(3):509–524. Hadi, A. S. and Ling, R. F. (1998). “Some Cautionary Notes on the Use of Principal Components Regression.” The American Statistician, 52(1):15–19. Hastie, T., Tibshirani, R., and Friedman, J. (2009). The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Springer series in statistics. Springer. Holm, S. (1979). “A Simple Sequentially Rejective Multiple Test Procedure.” Scandinavian journal of statistics, 65–70. Hwang, J. G. and Nettleton, D. (2003). “Principal Components Regression with Data Chosen Components and Related Methods.” Technometrics, 45(1). Inoue, A. and Kilian, L. (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, 103:511–522. Joliffe, I. T. (1982). “A Note on the Use of Principal Components in Regression.” Applied Statistics, 31(3):300–303. Kim, H. H. and Swanson, N. R. (2014). “Forecasting Financial and Macroeconomic Variables Using Data Reduction Methods: New Empirical Evidence.” Journal of Econometrics, 178(2):352–367. Li, K.-C. (1991). “Sliced Inverse Regression for Dimension reduction.” Journal of the American Statistical Association, 86:316–327. Mosteller, F. and Tukey, J. W. (1977). “Data Analysis and Regression: a Second Course in Statistics.” Addison-Wesley Series in Behavioral Science: Quantitative Methods. Ng, S. (2013). “Variable Selection in Predictive Regressions.” In Elliott, G. and Timmermann, A. (eds.), Handbook of Economic Forecasting, volume 2, Part B, chapter 14, 752 – 789. Elsevier. Onatski, A. (2010). “Determining the Number of Factors from Empirical Distribution of Eigenvalues.” The Review of Economics and Statistics, 92(4):1004–1016. Stock, J. H. and Watson, M. W. (2002a). “Forecasting Using Principal Components From a Large Number of Predictors.” Journal of the American Statistical Association, 97:1167–1179. Stock, J. H. and Watson, M. W. (2002b). “Macroeconomic Forecasting Using Diffusion Indexes.” Journal of Business & Economic Statistics, 20(2):147–62. Stock, J. H. and Watson, M.W. (2006). “Forecasting with Many Predictors.” In Elliott, G., Granger, C., and Timmermann, A. (eds.), Handbook of Economic Forecasting, volume 1, chapter 10, 515–554. Elsevier. Stock, J. H. and Watson, M.W. (2010). “Dynamic Factor Models.” In Clements, M. P. and Hendry, D. F. (eds.), Oxford Handbook of Economic Forecasting, volume 1, chapter 2. Oxford University Press, USA. Stock, J. H. andWatson, M.W. (2012a). “Disentangling the Channels of the 2007—09 Recession.” Brookings Papers on Economic Activity: Spring 2012, 81. Stock, J. H. and Watson, M. W. (2012b). “Generalized shrinkage methods for forecasting using many predictors.” Journal of Business & Economic Statistics, 30(4):481–493. |

URI: | https://mpra.ub.uni-muenchen.de/id/eprint/60673 |