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Macroeconomic Forecasting in the Era of Big Data pp 267–291Cite as

Subspace Methods

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Part of the book series: Advanced Studies in Theoretical and Applied Econometrics ((ASTA,volume 52))

Abstract

With increasingly many variables available to macroeconomic forecasters, dimension reduction methods are essential to obtain accurate forecasts. Subspace methods are a new class of dimension reduction methods that have been found to yield precise forecasts when applied to macroeconomic and financial data. In this chapter, we review three subspace methods: subset regression, random projection regression, and compressed regression. We provide currently available theoretical results, and indicate a number of open avenues. The methods are illustrated in various settings relevant to macroeconomic forecasters.

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References

  • Achlioptas, D. (2003). Database-friendly random projections: Johnson-Lindenstrauss with binary coins. Journal of Computer and System Sciences, 66(4), 671–687.

    Article  Google Scholar 

  • Bai, J., & Ng, S. (2006). Confidence intervals for diffusion index forecasts and inference for factor-augmented regressions. Econometrica, 74(4), 1133–1150.

    Article  Google Scholar 

  • Bai, J., & Ng, S. (2008). Forecasting economic time series using targeted predictors. Journal of Econometrics, 146(2), 304–317.

    Article  Google Scholar 

  • Bay, S. D. (1998). Combining nearest neighbor classifiers through multiple feature subsets. In Proceedings of the Fifteenth International Conference on Machine Learning ICML (vol. 98, pp. 37–45). San Francisco: Morgan Kaufmann.

    Google Scholar 

  • Bingham, E., & Mannila, H. (2001). Random projection in dimensionality reduction: Applications to image and text data. In Proceedings of the Seventh ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (pp. 245–250). New York: ACM.

    Chapter  Google Scholar 

  • Boot, T., & Nibbering, D. (2019). Forecasting using random subspace methods. Journal of Econometrics, 209(2), 391–406. https://doi.org/10.1016/j.jeconom.2019.01.009.

    Article  Google Scholar 

  • Boutsidis, C., Zouzias, A., Mahoney, M. W., & Drineas, P. (2015). Randomized dimensionality reduction for k-means clustering. IEEE Transactions on Information Theory, 61(2), 1045–1062.

    Article  Google Scholar 

  • Breiman, L. (1996). Bagging predictors. Machine Learning, 24(2), 123–140.

    Google Scholar 

  • Breiman, L. (1999). Pasting small votes for classification in large databases and on-line. Machine Learning, 36(1–2), 85–103.

    Article  Google Scholar 

  • Bryll, R., Gutierrez-Osuna, R., & Quek, F. (2003). Attribute bagging: Improving accuracy of classifier ensembles by using random feature subsets. Pattern Recognition, 36(6), 1291–1302.

    Article  Google Scholar 

  • Cannings, T. I., & Samworth, R. J. (2017). Random-projection ensemble classification. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 79(4), 959–1035.

    Article  Google Scholar 

  • Chiong, K. X., & Shum, M. (2018). Random projection estimation of discrete-choice models with large choice sets. Management Science, 65, 1–457.

    Google Scholar 

  • Claeskens, G., Magnus, J. R., Vasnev, A. L., & Wang, W. (2016). The forecast combination puzzle: a simple theoretical explanation. International Journal of Forecasting, 32(3), 754–762.

    Article  Google Scholar 

  • Dasgupta, S., & Gupta, A. (2003). An elementary proof of a theorem of Johnson and Lindenstrauss. Random Structures & Algorithms, 22(1), 60–65.

    Article  Google Scholar 

  • Elliott, G., Gargano, A., & Timmermann, A. (2013). Complete subset regressions. Journal of Econometrics, 177(2), 357–373.

    Article  Google Scholar 

  • Elliott, G., Gargano, A., & Timmermann, A. (2015). Complete subset regressions with large-dimensional sets of predictors. Journal of Economic Dynamics and Control, 54, 86–110.

    Article  Google Scholar 

  • Elliott, G., & Timmermann, A. (2013). Handbook of economic forecasting. Amsterdam: Elsevier.

    Google Scholar 

  • Fradkin, D., & Madigan, D. (2003). Experiments with random projections for machine learning. In Proceedings of the Ninth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (pp. 517–522). New York: ACM.

    Chapter  Google Scholar 

  • Frieze, A., Kannan, R., & Vempala, S. (2004). Fast Monte-Carlo algorithms for finding low-rank approximations. Journal of the Association for Computing Machinery, 51(6), 1025–1041.

    Article  Google Scholar 

  • Garcia, M. G., Medeiros, M. C., & Vasconcelos, G. F. (2017). Real-time inflation forecasting with high-dimensional models: The case of Brazil. International Journal of Forecasting, 33(3), 679–693.

    Article  Google Scholar 

  • Gillen, B. J. (2016). Subset optimization for asset allocation. Social Science Working Paper, 1421, California Institute of Technology, Pasadena

    Google Scholar 

  • Guhaniyogi, R., & Dunson, D. B. (2015). Bayesian compressed regression. Journal of the American Statistical Association, 110(512), 1500–1514.

    Article  Google Scholar 

  • Hansen, B. E. (2010). Averaging estimators for autoregressions with a near unit root. Journal of Econometrics, 158(1), 142–155.

    Article  Google Scholar 

  • Ho, T. K. (1998). The random subspace method for constructing decision forests. IEEE Transactions on Pattern Analysis and Machine Intelligence, 20(8), 832–844.

    Article  Google Scholar 

  • Johnson, W. B., & Lindenstrauss, J. (1984). Extensions of Lipschitz mappings into a Hilbert space. Contemporary Mathematics, 26(189–206), 1.

    Google Scholar 

  • Kabán, A. (2014). New bounds on compressive linear least squares regression. In Artificial intelligence and statistics (pp. 448–456). Boston: Addison-Wesley.

    Google Scholar 

  • Koop, G., Korobilis, D., & Pettenuzzo, D. (2019). Bayesian compressed vector autoregressions. Journal of Econometrics, 210(1), 135–154.

    Article  Google Scholar 

  • Leroux, M., Kotchoni, R., & Stevanovic, D. (2017). Forecasting economic activity in data-rich environment. University of Paris Nanterre, EconomiX.

    Google Scholar 

  • Li, P., Hastie, T. J., & Church, K. W. (2006). Very sparse random projections. In Proceedings of the 12th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (pp. 287–296). New York: ACM.

    Chapter  Google Scholar 

  • Mahoney, M. W., & Drineas, P. (2009). CUR matrix decompositions for improved data analysis. Proceedings of the National Academy of Sciences, 106(3), 697–702.

    Article  Google Scholar 

  • Maillard, O., & Munos, R. (2009). Compressed least-squares regression. In Advances in neural information processing systems (pp. 1213–1221). Cambridge: MIT Press.

    Google Scholar 

  • McCracken, M. W., & Ng, S. (2016). FRED-MD: A monthly database for macroeconomic research. Journal of Business & Economic Statistics, 34(4), 574–589.

    Article  Google Scholar 

  • Meligkotsidou, L., Panopoulou, E., Vrontos, I. D., & Vrontos, S. D. (2019). Out-of-sample equity premium prediction: A complete subset quantile regression approach. European Journal of Finance, 1–26.

    Google Scholar 

  • Ng, S. (2013). Variable selection in predictive regressions. Handbook of Economic Forecasting, 2(Part B), 752–789.

    Google Scholar 

  • Pick, A., & Carpay, M. (2018). Multi-step forecasting with large vector autoregressions. Working Paper.

    Google Scholar 

  • Schneider, M. J., & Gupta, S. (2016). Forecasting sales of new and existing products using consumer reviews: A random projections approach. International Journal of Forecasting, 32(2), 243–256.

    Article  Google Scholar 

  • Shen, W., & Wang, J. (2017). Portfolio selection via subset resampling. In Thirty-First AAAI Conference on Artificial Intelligence (pp. 1517–1523).

    Google Scholar 

  • Slawski, M. et al. (2018). On principal components regression, random projections, and column subsampling. Electronic Journal of Statistics, 12(2), 3673–3712.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Stock, J. H., & Watson, M. W. (2006). Forecasting with many predictors. Handbook of economic forecasting (vol. 1, pp. 515–554). Amsterdam: Elsevier.

    Google Scholar 

  • Thanei, G.-A., Heinze, C., & Meinshausen, N. (2017). Random projections for large-scale regression. In Big and complex data analysis (pp. 51–68). Berlin: Springer.

    Chapter  Google Scholar 

  • Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society. Series B (Methodological) 58,(1), 267–288.

    Google Scholar 

  • Timmermann, A. (2006). Forecast combinations. In Handbook of economic forecasting (vol. 1, pp. 135–196). Amsterdam: Elsevier.

    Chapter  Google Scholar 

  • Vempala, S. S. (2005). The random projection method.Series in discrete mathematics and theoretical computer science. Providence: American Mathematical Society.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Economics, Econometrics and Finance, University of Groningen, Groningen, The Netherlands

    Tom Boot

  2. Department of Econometrics and Business Statistics, Monash University, Clayton, VIC, Australia

    Didier Nibbering

Authors
  1. Tom Boot
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  2. Didier Nibbering
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Corresponding author

Correspondence to Tom Boot .

Editor information

Editors and Affiliations

  1. UHERO and Department of Economics, University of Hawaii at Manoa, Honolulu, HI, USA

    Peter Fuleky

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Boot, T., Nibbering, D. (2020). Subspace Methods. 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_9

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