Forecasting Brazilian macroeconomics variables using high-dimensional time series
DOI:
https://doi.org/10.1590/0101-41615013rrtKeywords:
Forecast, Diffusion Index, Shrinkage Methods, Forecast Combination, Brazilian MacroeconomicsAbstract
This paper analyzes the performance of high-dimensional factor models to forecast four Brazilian
macroeconomic variables: two real variables, unemployment rate and industrial production
index, and two nominal variables, IPCA and IPC. The factors are estimated from a data set
containing 117 macroeconomic variables. We applied techniques to improve factor models forecasts. Methods of statistical learning are applied aims to increase the performance of factors
models. Three types of statistical learning techniques are used: shrinkage methods, forecast
combinations, and selection of preditors. The factors are extracted using supervised and unsupervised
version. The results indicate that statistical learning improves forecasts performance.
The combination of statistical learning and supervised factor models is more accurate than all
other models, with exception to the industrial production index which is best forecasted by
unsupervised factor model without statistical learning.
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References
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Dias, F., Pinheiro, M. e Rua, A. “Forecasting using targeted diffusion indexes”, Journal of Forecasting 29, no.3: 341-352, 2010.
Efron, B., Hastie, T., Johnstone, L., and Tibshirani, R. “Least angle regression”. Annals of Statistics 32: 407-499, 2004.
Eickmeier, S. and Ziegler, C. “How successful are dynamic factor models at forecasting output and inflation? a meta-analytic approach”. Journal of Forecasting 27, no.3: 237-265, 2008.
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Pesaran, H. and Timmermann, A. “Selection of Estimation Window in The Presence of Breaks”, Journal of Econometrics 137, no.1: 134-161, 2007.
Pesaran, H.; Petenuzzo, D. e Timmermann, A. “Forecasting Time Series Subject To Multiple Structural Breaks” Review of Economic Studies 73: 1057-1084, 2006.
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Rossi, B. e Inoue, A. “Out-of-sample Forecast Tests Robust to The Window Size Choice”. Journal of Business and Economics Statistics 30, no.3: 432-453, 2012.
Saigo, H.; Uno, T. and Tsuda, K. “Mining Complex Genotypic Features for Predicting Hiv-1 Drug Resistance”, Bioinformatics 23: 2455–2462, 2007.
Stock, J. H. and Watson, M. W. “A Comparison of Linear and Nonlinear Univariate Models for Forecasting Macroeconomic Time Series”. In: Engle, R., White, H. (Eds.), Cointegration, Causality and Forecasting: A Festschrift for Clive W.J. Granger. Oxford University Press, 1999.
Stock, J. H. and Watson, M. W. “Forecasting Using Principal Components from a Large Number of Predictors”. Journal of the American Statistical Association 97: 1167-1179, 2002.
Stock, J. H. and Watson, M. W. “Combination Forecasts of Output Growth in a Seven Country Data Set”. Journal of Forecasting 23: 405-430, 2004.
Stock, J. H. and Watson, M. W. “Implications of Dynamic Factor Models for VAR Analysis”. Nber Working Papers 11467, 2005.
Stock, J. H. and Watson, M. W. “Forecasting With Many Predictors” In Elliott, G., Granger, C., and Timmermann, A., Editors, Handbook of Economic Forecasting 1, Chapter 10: 515-554, 2006.
Stock, J. H. and Watson, M. W. “Generalized Shrinkage Methods for Forecasting Using Many Predictors” Journal of Business and Economic Statistics 30, no.4: 481-493, 2012.
Tibshirani, R. “Regression Shrinkage and Selection via the Lasso”. Journal of the Royal Statistical Society, Series B, 58 p. 267-288, 1996.
Tu, Y., and Lee, T.H. “Forecasting Using Supervised Factor Models” Journal of Management Science and Engineering 4: 12-27, 2019.
Watson, M. And Amengual, D. “Consistent Estimation Of The Number Of Dynamic Factors In A Large N And T Panel” Journal of Business and Economic Statistics 25, no. 1: 91-96, 2007.
Yin, Shou-yung, Liu, Chu-an e Lin, C. “Focused Information Criterion And Model Averaging For Large Panels With A Multifactor Error Structure”, Ideas Working Paper: 16-a016, Institute Of Economics, Academia Sinica, 2016.
Yuan, M. and Lin, Y. 2007 “On the Non-negative Garrotte Estimator.” Journal of the Royal Statistical Society 69, no.2: 143-161.
Zou, H. “The Adaptive Lasso and Its Oracle Properties” Journal of the American Statistical Association 101: 1418-1429, 2006.
Zou, H. e Hastie, T. “Regularization and Variable Selection Via The Elastic Net”, Journal of the Royal Statistical Society, Series B Vol. 67, Part 2: 301–320, 2005.
Zhang, Ke; Yin, Fan E Xiong, S. “Comparisons of Penalized Least Squares Methods by Simulations”. Working Paper, Chinese Academy Of Sciences, 2014.
Bai, J. “Inferential theory for factor models of large dimensions”. Econometrica 71:135–171, 2003.
Bai, J. and Ng, S. “Determining the number of factors in approximate factor models”. Econometrica 70: 191–221, 2002.
Bai, J. and Ng, S. “Confidence intervals for diffusion index forecasts and inference for factoraugmented regressions”. Econometrica 74 1133–1150, 2006.
Bai, J. and Ng, S. “Forecasting economic time series using targeted predictors” Journal of Econometrics 146: 304–317, 2009.
Bai, J. and Ng, S. “Boosting diffusion indices”. Journal of Applied Econometrics 4: 607–629, 2008.
Bair, Eric, Hastie, T., Paul, D. e Tibsharani, R. “Prediction by supervised principal components”. Journal of the American Statistical Association 101, no. 473, 2006.
Boivin, J., and Ng, S. “Are more data always better for factor analysis?” Journal of Econometrics 132: 169–194, 2006.
Breiman, L. “Better subset regression using the nonnegative garrote”. Technometrics 37, no. 4: p. 373- 384, 1995.
Cheng, X. and Hansen, B. “Forecasting with factor-augmented regression: A frequentist model averaging approach”. Journal of Econometrics 186: 280-293, 2015.
Dias, F., Pinheiro, M. e Rua, A. “Forecasting using targeted diffusion indexes”, Journal of Forecasting 29, no.3: 341-352, 2010.
Efron, B., Hastie, T., Johnstone, L., and Tibshirani, R. “Least angle regression”. Annals of Statistics 32: 407-499, 2004.
Eickmeier, S. and Ziegler, C. “How successful are dynamic factor models at forecasting output and inflation? a meta-analytic approach”. Journal of Forecasting 27, no.3: 237-265, 2008.
Elliot, G. e Timmermann, A. “Economic forecasting”. Princeton University Press, New Jersey, 2016.
Fernandez, C., lLey, E. e Steel, M. “Benchmark priors for Bayesian model averaging”. Journal of Econometrics 100: 381-427, 2001.
Ferreira, R., Bierens, H. e Castelar, I. “Forecasting quarterly Brazilian GDP growth rate with linear and nonlinear diffusion index models”. EconomiA 6, no.3: 261-292, 2005.
Figueiredo, F. M. R. “Forecasting Brazilian inflation using a large data set” Brazilian Central Bank, working paper series 228, 2010.
Foster, D. e George, E. “The risk inflation criterion for multiple regression” The Annals of Statistics 22: 1947-1975, 1994.
Garcia, M. Medeiros, M. e Vasconcelos, G. 2016 “Real-time inflation forecasting with high dimensional models: The case of Brazil”. XVI Encontro de Finanças, Rio de Janeiro.
Gelper, S. and Croux, C.2008 “Least angle regression for time series forecasting with many predictors”, Working paper. technical report, Katholieke Universiteit Leuven.
Hansen, B. “Least squares model averaging”. Econometrica 75: 1175–1189, 2007.
Hansen, B. “Least squares forecasting averaging”. Journal of Econometrics 146: 342–350, 2008.
Hansen, B. e Racine, J.S. “Jackknife model averaging”. Journal of Econometrics 167: 38–46, 2012.
Hansen, P. Lunde, A. e Nason, J. M. “The model confidence set”. Econometrica 79: 453-497, 2011.
Hastie, T.; Tibshirani, R. e Friedman, J. “The elements of statistical learning: data mining, inference, and prediction”. Springer-Verlag New York. 2ª ed, 2009.
Hillebrand, e.; Huang, Y.; Lee, t.; Li, C. “Using the entire yield curve in forecasting output and inflation”, Econometrics 6, no. 40, 2018.
Inoue, A., e Kilian, L. “How useful is bagging in forecasting economics time series? a case study of us cpi inflation”. J. Amer. Statist. Assoc. 103: 511–522, 2008.
Kim, H., e Swanson, N. “Forecasting financial and macroeconomic variables using data reduction methods: new empirical evidence”. Journal of Econometrics 178: 352–367, 2014.
Kim, H., e Swanson, N. “Mining big data using parsimonious factor machine learning, variable selection, and shrinkage methods”, Rutgers University, working paper, 2016.
Koop, G. and Potter, S. “Forecasting in dynamic factor models using Bayesian model averaging”. Econometrics Journal 7: 550-565, 2004.
Liu, C. E Kuo, B. “Model Averaging In Predictive Regressions”. Econometrics Journal 19, no.2: 203-231, 2016.
Kwiatkowski, D; Phillips, P.; Schmidt, P. e Shin, Y. “Testing the Null Hypothesis of Stationarity against the Alternative of a Unit Root”. Journal of Econometrics 54, no.9: 159-178, 1992.
Mallows, C.L. “Some Comments on Cp” Technometrics 15: 661–675, 1973.
Marcellino, M. A. “Comparison of Time Series Model Forecasting GDP Growth and Inflation”. Journal of Forecasting 27: 305-340, 2008.
Medeiros, M. C.; Vasconcelos, G. and Freitas, E. “Forecasting Brazilian Inflation with High-dimensional Models”. Brazilian Econometric Review 36, no 2. 2016.
Pesaran, H. and Timmermann, A. “Selection of Estimation Window in The Presence of Breaks”, Journal of Econometrics 137, no.1: 134-161, 2007.
Pesaran, H.; Petenuzzo, D. e Timmermann, A. “Forecasting Time Series Subject To Multiple Structural Breaks” Review of Economic Studies 73: 1057-1084, 2006.
Rahal, C. “Housing Market Forecasting With Factor Combinations”, Discussion Papers 15-05r, 2015, Department of Economics, University Of Birmingham.
Rossi, B. Advances in Forecasting Under Instability. In Elliott, G. and Timmermann, A., Editors, Handbook of Economic Forecasting, Volume 2b, Chapter 21: 1203-1324, 2012.
Rossi, B. e Inoue, A. “Out-of-sample Forecast Tests Robust to The Window Size Choice”. Journal of Business and Economics Statistics 30, no.3: 432-453, 2012.
Saigo, H.; Uno, T. and Tsuda, K. “Mining Complex Genotypic Features for Predicting Hiv-1 Drug Resistance”, Bioinformatics 23: 2455–2462, 2007.
Stock, J. H. and Watson, M. W. “A Comparison of Linear and Nonlinear Univariate Models for Forecasting Macroeconomic Time Series”. In: Engle, R., White, H. (Eds.), Cointegration, Causality and Forecasting: A Festschrift for Clive W.J. Granger. Oxford University Press, 1999.
Stock, J. H. and Watson, M. W. “Forecasting Using Principal Components from a Large Number of Predictors”. Journal of the American Statistical Association 97: 1167-1179, 2002.
Stock, J. H. and Watson, M. W. “Combination Forecasts of Output Growth in a Seven Country Data Set”. Journal of Forecasting 23: 405-430, 2004.
Stock, J. H. and Watson, M. W. “Implications of Dynamic Factor Models for VAR Analysis”. Nber Working Papers 11467, 2005.
Stock, J. H. and Watson, M. W. “Forecasting With Many Predictors” In Elliott, G., Granger, C., and Timmermann, A., Editors, Handbook of Economic Forecasting 1, Chapter 10: 515-554, 2006.
Stock, J. H. and Watson, M. W. “Generalized Shrinkage Methods for Forecasting Using Many Predictors” Journal of Business and Economic Statistics 30, no.4: 481-493, 2012.
Tibshirani, R. “Regression Shrinkage and Selection via the Lasso”. Journal of the Royal Statistical Society, Series B, 58 p. 267-288, 1996.
Tu, Y., and Lee, T.H. “Forecasting Using Supervised Factor Models” Journal of Management Science and Engineering 4: 12-27, 2019.
Watson, M. And Amengual, D. “Consistent Estimation Of The Number Of Dynamic Factors In A Large N And T Panel” Journal of Business and Economic Statistics 25, no. 1: 91-96, 2007.
Yin, Shou-yung, Liu, Chu-an e Lin, C. “Focused Information Criterion And Model Averaging For Large Panels With A Multifactor Error Structure”, Ideas Working Paper: 16-a016, Institute Of Economics, Academia Sinica, 2016.
Yuan, M. and Lin, Y. 2007 “On the Non-negative Garrotte Estimator.” Journal of the Royal Statistical Society 69, no.2: 143-161.
Zou, H. “The Adaptive Lasso and Its Oracle Properties” Journal of the American Statistical Association 101: 1418-1429, 2006.
Zou, H. e Hastie, T. “Regularization and Variable Selection Via The Elastic Net”, Journal of the Royal Statistical Society, Series B Vol. 67, Part 2: 301–320, 2005.
Zhang, Ke; Yin, Fan E Xiong, S. “Comparisons of Penalized Least Squares Methods by Simulations”. Working Paper, Chinese Academy Of Sciences, 2014.
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Copyright (c) 2020 Rafael Barros Barbosa, Roberto Tatiwa Ferreira, Thibério Mota da Silva
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Conselho Nacional de Desenvolvimento Científico e Tecnológico
Grant numbers 306030/2016-0
How to Cite
Barbosa, R. B., Ferreira, R. T., & Silva, T. M. da. (2020). Forecasting Brazilian macroeconomics variables using high-dimensional time series. Estudos Econômicos (São Paulo), 50(1), 67-98. https://doi.org/10.1590/0101-41615013rrt
Atualizado em 14/08/2025