Empirical Economics

, Volume 58, Issue 1, pp 169–190 | Cite as

Forecasting with supervised factor models

  • Simon Lineu UmbachEmail author


A conventional approach to forecast in a data-rich environment is to estimate factor-augmented predictive regressions with factors constructed by principal component analysis. This study analyzes under which circumstances gains in forecast accuracy can be achieved by incorporating some form of supervision in the factor estimation process. Specifically, principal covariate regression (PCovR) is considered. For the problem of choosing a value for the supervision parameter in PCovR, an information criterion is proposed. The information criterion is shown to be an appropriate means to find a good balance between predictor space compression and target orientation of the estimated factors. A simulation study and an empirical application on a macroeconomic dataset show that supervised factors can improve the forecasting accuracy of factor models.


Factor model Principal covariate regression Principal components Forecasting 



I would like to thank Prof. Jörg Breitung for valuable discussion and helpful suggestions. I also thank the editor Prof. Kunst and two anonymous referees for useful comments.

Compliance with Ethical Standards

Conflict of interest

The author declares that he has no conflict of interest.


  1. Bai J, Ng S (2002) Determining the number of factors in approximate factor models. Econometrica 70(1):191–221CrossRefGoogle Scholar
  2. Boivin J, Ng S (2006) Are more data always better for factor analysis? J Econ 132(1):169–194CrossRefGoogle Scholar
  3. Breitung J, Choi I (2013) Factor models. Handbook of research methods and applications in empirical macroeconomics, vol 11. Edward Elgar Publishing, Cheltenham, pp 249–265CrossRefGoogle Scholar
  4. Breitung J, Roling C (2015) Forecasting inflation rates using daily data: a nonparametric midas approach. J Forecast 34(7):588–603CrossRefGoogle Scholar
  5. de Jong S, Kiers HAL (1992) Principal covariates regression: part I. Theory. Chemometr Intell Lab Syst 14:155–164CrossRefGoogle Scholar
  6. Heij C, Groenen PJ, van Dijk D (2007) Forecast comparison of principal component regression and principal covariate regression. Comput Stat Data Anal 51(7):3612–3625CrossRefGoogle Scholar
  7. Hurvich CM, Simonoff JS, Tsai CL (1998) Smoothing parameter selection in nonparametric regression using an improved akaike information criterion. J R Stat Soc Seri B (Statistical Methodology) 60(2):271–293CrossRefGoogle Scholar
  8. McCracken MW, Ng S (2016) FRED-MD: a monthly database for macroeconomic research. J Bus Econ Stat 34(4):574–589CrossRefGoogle Scholar
  9. Stock JH, Watson MW (2002) Macroeconomic forecasting using diffusion indexes. J Bus Econ Stat 20(2):147–162CrossRefGoogle Scholar
  10. Stock JH, Watson MW (2006) Forecasting with many predictors. In: Elliott G, Granger C, Timmermann A (eds) Handbook of economic forecasting, vol 1, 1st edn. Elsevier, Amsterdam, pp 515–554CrossRefGoogle Scholar
  11. Vervloet M, Deun KV, den Noortgate WV, Ceulemans E (2013) On the selection of the weighting parameter value in principal covariates regression. Chemometr Intell Lab Syst 123:36–43CrossRefGoogle Scholar
  12. Vervloet M, Kiers H, den Noortgate WV, Ceulemans E (2015) PCovR: an R package for principal covariates regression. J Stat Softw 65(1):1–14Google Scholar
  13. Wilderjans T, Ceulemans E, Mechelen IV (2009) Simultaneous analysis of coupled data blocks differing in size: a comparison of two weighting schemes. Comput Stat Data Anal 53(4):1086–1098CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Cologne Graduate School in Management, Economics and Social SciencesUniversity of CologneCologneGermany

Personalised recommendations