Skip to main content
SpringerLink
Log in

Prediction of Quantiles by Statistical Learning and Application to GDP Forecasting

  • Conference paper
Discovery Science (DS 2012)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 7569))

Included in the following conference series:

Abstract

In this paper, we tackle the problem of prediction and confidence intervals for time series using a statistical learning approach and quantile loss functions. In a first time, we show that the Gibbs estimator is able to predict as well as the best predictor in a given family for a wide set of loss functions. In particular, using the quantile loss function of [1], this allows to build confidence intervals. We apply these results to the problem of prediction and confidence regions for the French Gross Domestic Product (GDP) growth, with promising results.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Koenker, R., Bassett, G.J.: Regression quantiles. Econometrica 46, 33–50 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  2. Hamilton, J.: Time Series Analysis. Princeton University Press (1994)

    Google Scholar 

  3. Brockwell, P., Davis, R.: Time Series: Theory and Methods, 2nd edn. Springer (2009)

    Google Scholar 

  4. Cesa-Bianchi, N., Lugosi, G.: Prediction, Learning, and Games. Cambridge University Press, New York (2006)

    Book  MATH  Google Scholar 

  5. Stoltz, G.: Agrégation séquentielle de prédicteurs: méthodologie générale et applications à la prévision de la qualité de l’air et à celle de la consommation électrique. Journal de la SFDS 151(2), 66–106 (2010)

    MathSciNet  Google Scholar 

  6. Modha, D.S., Masry, E.: Memory-universal prediction of stationary random processes. IEEE Transactions on Information Theory 44(1), 117–133 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  7. Meir, R.: Nonparametric time series prediction through adaptive model selection. Machine Learning 39, 5–34 (2000)

    Article  MATH  Google Scholar 

  8. Alquier, P., Wintenberger, O.: Model selection for weakly dependent time series forecasting. Bernoulli 18(3), 883–913 (2012)

    Google Scholar 

  9. Biau, G., Patra, B.: Sequential quantile prediction of time series. IEEE Transactions on Information Theory 57, 1664–1674 (2011)

    Article  MathSciNet  Google Scholar 

  10. Dalalyan, A., Tsybakov, A.: Aggregation by exponential weighting, sharp PAC-Bayesian bounds and sparsity. Machine Learning 72, 39–61 (2008)

    Article  Google Scholar 

  11. Gerchinovitz, S.: Sparsity regret bounds for individual sequences in online linear regression. In: Proceedings of COLT 2011 (2011)

    Google Scholar 

  12. Catoni, O.: Statistical Learning Theory and Stochastic Optimization. Springer Lecture Notes in Mathematics (2004)

    Google Scholar 

  13. Catoni, O.: PAC-Bayesian Supervised Classification (The Thermodynamics of Statistical Learning). Lecture Notes-Monograph Series, vol. 56. IMS (2007)

    Google Scholar 

  14. Littlestone, N., Warmuth, M.: The weighted majority algorithm. Information and Computation 108, 212–261 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  15. Vovk, V.G.: Aggregating strategies. In: Proceedings of the 3rd Annual Workshop on Computational Learning Theory (COLT), pp. 372–283 (1990)

    Google Scholar 

  16. Koenker, R.: Quantile Regression. Cambridge University Press, Cambridge (2005)

    Book  MATH  Google Scholar 

  17. Belloni, A., Chernozhukov, V.: L1-penalized quantile regression in high-dimensional sparse models. The Annals of Statistics 39(1), 82–130 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  18. Shawe-Taylor, J., Williamson, R.: A PAC analysis of a bayes estimator. In: Proceedings of the Tenth Annual Conference on Computational Learning Theory, COLT 1997, pp. 2–9. ACM (1997)

    Google Scholar 

  19. McAllester, D.A.: PAC-Bayesian model averaging. In: Procs. of of the 12th Annual Conf. on Computational Learning Theory, Santa Cruz, California (Electronic), pp. 164–170. ACM, New York (1999)

    Google Scholar 

  20. Alquier, P.: PAC-Bayesian bounds for randomized empirical risk minimizers. Mathematical Methods of Statistics 17(4), 279–304 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  21. Audibert, J.Y.: PAC-Bayesian aggregation and multi-armed bandits. HDR Université Paris Est (2010)

    Google Scholar 

  22. Audibert, J.Y., Catoni, O.: Robust linear least squares regression. The Annals of Statistics 39(5), 2766–2794 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  23. Dedecker, J., Doukhan, P., Lang, G., León, J.R., Louhichi, S., Prieur, C.: Weak Dependence, Examples and Applications. Lecture Notes in Statistics, vol. 190. Springer, Berlin (2007)

    Google Scholar 

  24. Doukhan, P.: Mixing. Lecture Notes in Statistics. Springer, New York (1994)

    Book  MATH  Google Scholar 

  25. Catoni, O.: A PAC-Bayesian approach to adaptative classification. Preprint Laboratoire de Probabilités et Modèles Aléatoires (2003)

    Google Scholar 

  26. Devilliers, M.: Les enquêtes de conjoncture. In: Archives et Documents. Number 101, INSEE (1984)

    Google Scholar 

  27. Clavel, L., Minodier, C.: A monthly indicator of the french business climate. Documents de Travail de la DESE (2009)

    Google Scholar 

  28. Dubois, E., Michaux, E.: Étalonnages à l’aide d’enquêtes de conjoncture: de nouvaux résultats. In: Économie et Prévision. Number 172. INSEE (2006)

    Google Scholar 

  29. Biau, G., Biau, O., Rouvière, L.: Nonparametric forecasting of the manufacturing output growth with firm-level survey data. Journal of Business Cycle Measurement and Analysis 3, 317–332 (2008)

    Article  Google Scholar 

  30. Diebold, F.X., Tay, A.S., Wallis, K.F.: Evaluating density forecasts of inflation: the survey of professional forecasters. Discussion Paper No.48, ESRC Macroeconomic Modelling Bureau, University of Warwick and Working Paper No.6228, National Bureau of Economic Research, Cambridge, Mass. (1997)

    Google Scholar 

  31. Tay, A.S., Wallis, K.F.: Density forecasting: a survey. Journal of Forecasting 19, 235–254 (2000)

    Article  Google Scholar 

  32. Britton, E., Fisher, P., Whitley, J.: The inflation report projections: Understanding the fan chart. Bank of England Quarterly Bulletin 38(1), 30–37 (1998)

    Google Scholar 

  33. Cornec, M.: Constructing a conditional gdp fan chart with an application to french business survey data. In: 30th CIRET Conference, New York (2010)

    Google Scholar 

  34. Dowd, K.: The inflation fan charts: An evaluation. Greek Economic Review 23, 99–111 (2004)

    Google Scholar 

  35. Li, X.: Agrégation de prédicteurs appliquée à la conjoncture. Rapport de stage de M2 - Université Paris 6 - INSEE sous la direction de Matthieu Cornec (2010)

    Google Scholar 

  36. Casella, G., Robert, C.: Monte Carlo Statistical Methods, 2nd edn. Springer (2004)

    Google Scholar 

  37. R Development Core Team: R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna (2008)

    Google Scholar 

  38. Rio, E.: Ingalités de Hoeffding pour les fonctions lipschitziennes de suites dépendantes. Comptes Rendus de l’Académie des Sciences de Paris, Série I 330, 905–908 (2000)

    MathSciNet  MATH  Google Scholar 

  39. Wintenberger, O.: Deviation inequalities for sums of weakly dependent time series. Electronic Communications in Probability 15, 489–503 (2010)

    MathSciNet  MATH  Google Scholar 

  40. Seldin, Y., Laviolette, F., Cesa-Bianchi, N., Auer, P., Shawe-Taylor, J.: PAC-Bayesian inequalities for martingales. Preprint arXiv:1110.6886 (2011)

    Google Scholar 

  41. Kullback, S.: Information theory and statistics. Wiley, New York (1959)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. LPMA (Université Paris 7), 175, rue du Chevaleret, 75013, Paris, France

    Pierre Alquier

  2. Laboratoire de Mathématiques (Université de Cergy-Pontoise), UCP site Saint-Martin, 2 boulevard Adolphe Chauvin, 95000, Cergy-Pontoise, France

    Xiaoyin Li

  3. CREST (ENSAE), France

    Pierre Alquier

Authors
  1. Pierre Alquier
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xiaoyin Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. LIP6 laboratory, Parix VI University, 4, place Jussieu, 75005, Paris, France

    Jean-Gabriel Ganascia

  2. Telecom Bretagne, UMR 6285 Lab-STICC, Technopôle Brest-Iroise - CS 83818, 29238, Brest Cedex 3, France

    Philippe Lenca

  3. INSA Lyon, UMR 5205 LIRIS, 7, avenue Jean Capelle, 69621, Villeurbanne Cedex, France

    Jean-Marc Petit

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Alquier, P., Li, X. (2012). Prediction of Quantiles by Statistical Learning and Application to GDP Forecasting. In: Ganascia, JG., Lenca, P., Petit, JM. (eds) Discovery Science. DS 2012. Lecture Notes in Computer Science(), vol 7569. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33492-4_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-33492-4_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33491-7

  • Online ISBN: 978-3-642-33492-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation