Abstract
Factor models are widely used in macroeconomic forecasting. With large datasets, factor models are particularly useful due to their intrinsic dimension reduction. In this chapter, we consider the forecasting problem using factor models, with special consideration to large datasets. In factor model estimation, we focus on principal component methods, and show how the estimated factors can be used to assist forecasting. Machine learning methods are discussed to encompass the high-dimensional features of large factor models. We consider policy evaluation as a nowcasting problem and show how factor analysis can be used to perform counter-factual outcome prediction in complicated models with observational data. The usage of all these techniques is illustrated by empirical examples.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Another popular forecasting strategy is the so-called “rolling” scheme, which, in each step, drops the earliest observation in the current forecast window while adding a new one. The relative performance between the recursive and rolling schemes can be found in, for example, Kim and Swanson (2018).
- 2.
Readers need to be cautious to understand and interpret the results of comparing different forecasting methods. For instance, each entry in Table 8.5 corresponds to the best performance of a given method, say PCA, ICA, or SPCA, across a variety of machine learning models, which are used to forecast the target variables using the extracted factors. This implies that the reported forecasting errors in the table already take into account the data to forecast, due to the selection over the machine learning models. However, the relative forecasting performances across PCA, ICA, and SPCA may be different when we “truly” forecast out of sample.
References
Back, A. D., & Weigend, A. S. (1997). A first application of independent component analysis to extracting structure from stock returns. International Journal of Neural Systems, 8(4), 473–484.
Bai, J. (2003). Inferential theory for factor models of large dimensions. Econometrica, 71(1), 135–171.
Bai, J. (2009). Panel data models with interactive fixed effects. Econometrica, 77(4), 1229–1279.
Bai, J., & Ng, S. (2002). Determining the number of factors in approximate factor models. Econometrica, 70(1), 191–221.
Bai, J., & Ng, S. (2006). Confidence intervals for diffusion index forecasts and inference for factor-augmented regressions. Econometrica, 74(4), 1133–1150.
Bai, J., & Ng, S. (2008). Forecasting economic time series using targeted predictors. Journal of Econometrics, 146(2), 304–317.
Bai, J., & Ng, S. (2009). Boosting diffusion indices. Journal of Applied Econometrics, 24(4), 607–629.
Bartlett, M. S., Movellan, J. R., & Sejnowski, T. J. (2002). Face recognition by independent component analysis. IEEE Transactions on Neural Networks, 13(6), 1450–1464.
Brown, G. D., Yamada, S., & Sejnowski, T. J. (2001). Independent component analysis at the neural cocktail party. Trends in Neurosciences, 24(1), 54–63.
Cai, T. T., Ma, Z., & Wu, Y. (2013). Sparse PCA: Optimal rates and adaptive estimation. The Annals of Statistics, 41(6), 3074–3110.
Chun, H., & Keleş, 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.
Efron, B., Hastie, T., Johnstone, I., & Tibshirani, R. (2004). Least angle regression. The Annals of Statistics, 32(2), 407–499.
Firpo, S., & Possebom, V. (2018). Synthetic control method: Inference, sensitivity analysis and confidence sets. Journal of Causal Inference, 6(2), 1–26.
Fuentes, J., Poncela, P., & Rodríguez, J. (2015). Sparse partial least squares in time series for macroeconomic forecasting. Journal of Applied Econometrics, 30(4), 576–595.
Gobillon, L., & Magnac, T. (2016). Regional policy evaluation: Interactive fixed effects and synthetic controls. Review of Economics and Statistics, 98(3), 535–551.
Hastie, T., Tibshirani, R., & Friedman, J. (2009). The elements of statistical learning: Data mining, inference, and prediction. Berlin: Springer.
Hastie, T., Tibshirani, R., & Wainwright, M. (2015). Statistical learning with sparsity: The lasso and generalizations. London: Chapman and Hall/CRC.
Hotelling, H. (1933). Analysis of a complex of statistical variables into principal components. Journal of Educational Psychology, 24(6), 417–441.
Hsiao, C., Ching, H. S., & Wan, S. K. (2012). A panel data approach for program evaluation: Measuring the benefits of political and economic integration of Hong Kong with mainland China. Journal of Applied Econometrics, 27(5), 705–740.
Hyvärinen, A. (1999). Fast and robust fixed-point algorithms for independent component analysis. IEEE Transactions on Neural Networks, 10(3), 626–634.
Hyvärinen, A., & Oja, E. (2000). Independent component analysis: Algorithms and applications. Neural Networks, 13(4–5), 411–430.
Jolliffe, I. T. (2002). Principal component analysis. Berlin: Springer.
Jolliffe, I. T., & Cadima, J. (2016). Principal component analysis: A review and recent developments. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 374(2065), 20150202.
Kim, D., & Oka, T. (2014). Divorce law reforms and divorce rates in the USA: An interactive fixed-effects approach. Journal of Applied Econometrics, 29(2), 231–245.
Kim, H. H., & Swanson, N. R. (2018). Mining big data using parsimonious factor, machine learning, variable selection and shrinkage methods. International Journal of Forecasting, 34(2), 339–354.
Li, H., Li, Q., & Shi, Y. (2017). Determining the number of factors when the number of factors can increase with sample size. Journal of Econometrics, 197(1), 76–86.
Muirhead, R. J. (2009). Aspects of multivariate statistical theory. Hoboken: Wiley.
Pearson, K. (1901). On lines and planes of closest fit to systems of points in space. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 2(11), 559–572.
Robbins, M. W., Saunders, J., & Kilmer B. (2017). A framework for synthetic control methods with high-dimensional, micro-level data: Evaluating a neighborhood-specific crime intervention. Journal of the American Statistical Association, 112(517), 109–126.
Stock, J. H., & Watson, M. W. (1999). Forecasting inflation. Journal of Monetary Economics, 44(2), 293–335.
Stock, J. H., & Watson, M. W. (2002a). Forecasting using principal components from a large number of predictors. Journal of the American Statistical Association, 97(460), 1167–1179.
Stock, J. H., & Watson, M. W. (2002b). Macroeconomic forecasting using diffusion indexes. Journal of Business & Economic Statistics, 20(2), 147–162.
Stock, J. H., & Watson, M. W. (2012). Generalized shrinkage methods for forecasting using many predictors. Journal of Business & Economic Statistics, 30(4), 481–493.
Stone, J. V. (2004). Independent component analysis: A tutorial introduction. Cambridge: MIT Press.
Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society Series B, 58(1), 267–288.
Tong, L., Liu, R. W., Soon, V. C., & Huang, Y. F. (1991). Indeterminacy and identifiability of blind identification. IEEE Transactions on Circuits and Systems, 38(5), 499–509.
Xu, Y. (2017). Generalized synthetic control method: Causal inference with interactive fixed effects models. Political Analysis, 25(1), 57–76.
Zou, H., & Hastie, T. (2005). Regularization and variable selection via the elastic net. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 67, 301–320.
Zou, H., Hastie, T., & Tibshirani, R. (2006). Sparse principal component analysis. Journal of Computational and Graphical Statistics, 15(2), 265–286.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Cao, J., Gu, C., Wang, Y. (2020). Principal Component and Static Factor Analysis. In: Fuleky, P. (eds) Macroeconomic Forecasting in the Era of Big Data. Advanced Studies in Theoretical and Applied Econometrics, vol 52. Springer, Cham. https://doi.org/10.1007/978-3-030-31150-6_8
Download citation
DOI: https://doi.org/10.1007/978-3-030-31150-6_8
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-31149-0
Online ISBN: 978-3-030-31150-6
eBook Packages: Economics and FinanceEconomics and Finance (R0)