Probabilistic Quantile Factor Analysis

Korobilis, Dimitris and Schroeder, Maximilian (2024): Probabilistic Quantile Factor Analysis.

Abstract

This paper extends quantile factor analysis to a probabilistic variant that incorporates regularization and computationally efficient variational approximations. We establish through synthetic and real data experiments that the proposed estimator can, in many cases, achieve better accuracy than a recently proposed loss-based estimator. We contribute to the factor analysis literature by extracting new indexes of low, medium, and high economic policy uncertainty, as well as loose, median, and tight financial conditions. We show that the high uncertainty and tight financial conditions indexes have superior predictive ability for various measures of economic activity. In a high-dimensional exercise involving about 1000 daily financial series, we find that quantile factors also provide superior out-of-sample information compared to mean or median factors.

• Item Type: MPRA Paper
• Language: English
• Keywords: variational Bayes; penalized factors; quantile regression
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C11 - Bayesian Analysis: General; C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables > C31 - Cross-Sectional Models ; Spatial Models ; Treatment Effect Models ; Quantile Regressions ; Social Interaction Models; 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 > C5 - Econometric Modeling > C52 - Model Evaluation, Validation, and Selection; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C53 - Forecasting and Prediction Methods ; Simulation Methods

References

Adrian, T., Boyarchenko, N., and Giannone, D. (2019). Vulnerable growth. American Economic Review, 109(4):1263–89.

Aliverti, E. and Russo, M. (2022). Stratified stochastic variational inference for high-dimensional network factor model. Journal of Computational and Graphical Statistics, 31(2):502–511.

Ando, T. and Bai, J. (2020). Quantile co-movement in financial markets: A panel quantile model with unobserved heterogeneity. Journal of the American Statistical Association, 115(529):266–279.

Andreou, E., Ghysels, E., and Kourtellos, A. (2013). Should macroeconomic forecasters use daily financial data and how? Journal of Business & Economic Statistics, 31(2):240–251.

Bai, J. and Ng, S. (2002). Determining the number of factors in approximate factor models. Econometrica, 70(1):191–221.

Baker, S. R., Bloom, N., and Davis, S. J. (2016). Measuring economic policy uncertainty. The Quarterly Journal of Economics, 131(4):1593–1636.

Bates, B. J., Plagborg-Møller, M., Stock, J. H., and Watson, M. W. (2013). Consistent factor estimation in dynamic factor models with structural instability. Journal of Econometrics, 177(2):289–304.

Bernanke, B. S., Boivin, J., and Eliasz, P. (2005). Measuring the effects of monetary policy: A factor-augmented vector autoregressive (FAVAR) approach. The Quarterly Journal of Economics, 120(1):387–422.

Bhattacharya, A. and Dunson, D. B. (2011). Sparse Bayesian infinite factor models. Biometrika, pages 291–306.

Bishop, C. (1999). Variational principal components. In 1999 Ninth International Conference on Artificial Neural Networks ICANN 99. (Conf. Publ. No. 470), volume 1, pages 509–514.

Blei, D. M., Kucukelbir, A., and McAuliffe, J. D. (2017). Variational inference: A review for statisticians. Journal of the American Statistical Association, 112(518):859–877.

Carvalho, C. M., Chang, J., Lucas, J. E., Nevins, J. R., Wang, Q., and West, M. (2008). High-dimensional sparse factor modeling: Applications in gene expression genomics. Journal of the American Statistical Association, 103(484):1438–1456.

Carvalho, C. M., Polson, N. G., and Scott, J. G. (2010). The horseshoe estimator for sparse signals. Biometrika, 97(2):465–480.

Chen, L., Dolado, J. J., and Gonzalo, J. (2021). Quantile factor models. Econometrica, 89(2):875–910.

Clark, T. E., Huber, F., Koop, G., Marcellino, M., and Pfarrhofer, M. (2021). Investigating growth at risk using a multi-country non-parametric quantile factor model. Working paper.

George, E. I. and McCulloch, R. E. (1993). Variable selection via Gibbs sampling. Journal of the American Statistical Association, 88(423):881–889.

Gerlach, R. H., Chen, C. W. S., and Chan, N. Y. C. (2011). Bayesian time-varying quantile forecasting for value-at-risk in financial markets. Journal of Business & Economic Statistics, 29(4):481–492.

Ghahramani, Z. and Beal, M. J. (1999). Variational inference for Bayesian mixtures of factor analysers. In Proceedings of the 12th International Conference on Neural Information Processing Systems, NIPS'99, pages 449–455, Cambridge, MA, USA. MIT Press.

Gunawan, D., Kohn, R., and Nott, D. (2021). Variational Bayes approximation of factor stochastic volatility models. International Journal of Forecasting, 37(4):1355–1375.

Hoffman, M. D., Blei, D. M., Wang, C., and Paisley, J. (2013). Stochastic variational inference. Journal of Machine Learning Research, 14(40):1303–1347.

Iacopini, M., Ravazzolo, F., and Rossini, L. (2022). Bayesian multivariate quantile regression with alternative time-varying volatility specifications. Working paper.

Knowles, D. and Ghahramani, Z. (2011). Nonparametric Bayesian sparse factor models with application to gene expression modeling. The Annals of Applied Statistics, 5(2B):1534–1552.

Koenker, R. (2005). Quantile Regression. Econometric Society Monographs. Cambridge University Press.

Koop, G. and Korobilis, D. (2014). A new index of financial conditions. European Economic Review, 71:101–116.

Koop, G. and Korobilis, D. (2023). Bayesian dynamic variable selection in high-dimensions. International Economic Review, 64(3):1047–1074.

Korobilis, D. (2017). Quantile regression forecasts of inflation under model uncertainty. International Journal of Forecasting, 33(1):11–20.

Kose, M. A., Otrok, C., and Whiteman, C. H. (2003). International business cycles: World, region, and country-specific factors. American Economic Review, 93(4):1216–1239.

Lim, D., Park, B., Nott, D., Wang, X., and Choi, T. (2020). Sparse signal shrinkage and outlier detection in high-dimensional quantile regression with variational Bayes. Statistics and Its Interface, 13(2):237–249.

López-Salido, J. D. and Loria, F. (2019). Inflation at risk. Discussion Papers No. 14074, Center for Economic Policy Research.

Lütkepohl, H. (2005). New Introduction to Multiple Time Series Analysis. Number 978-3-540-27752-1 in Springer Books. Springer.

Mariano, R. S. and Murasawa, Y. (2003). A new coincident index of business cycles based on monthly and quarterly series. Journal of Applied Econometrics, 18(4):427–443.

Park, T. and Casella, G. (2008). The Bayesian lasso. Journal of the American Statistical Association, 103(482):681–686.

Ročková, V. and George, E. I. (2016). Fast Bayesian factor analysis via automatic rotations to sparsity. Journal of the American Statistical Association, 111(516):1608–1622.

Sargent, T. J. and Sims, C. A. (1977). Business Cycle Modeling Without Pretending to Have Too Much A Priori Economic Theory. Federal Reserve Bank of Minneapolis.

Stock, J. H. and Watson, M. W. (2002). Forecasting using principal components from a large number of predictors. Journal of the American Statistical Association, 97(460):1167–1179.

Tipping, M. E. (2001). Sparse Bayesian learning and the relevance vector machine. Journal of Machine Learning Research, 1:211–244.

Tsay, R. S., Peña, D., and Pankratz, A. E. (2000). Outliers in multivariate time series. Biometrika, 87(4):789–804.

West, M. (2003). Bayesian factor regression models in the "large p, small n" paradigm. In Bernardo, J., Bayarri, M., Berger, J., Dawid, A., Heckerman, D., Smith, A., and West, M., editors, Bayesian Statistics 7, pages 723–732. Oxford University Press.

Yu, K. and Moyeed, R. A. (2001). Bayesian quantile regression. Statistics & Probability Letters, 54(4):437–447.