Skip to main content
SpringerLink
Log in
Book cover

Complex Models and Computational Methods in Statistics pp 63–76Cite as

Theoretical Regression Trees: A Tool for Multiple Structural-Change Models Analysis

  • Chapter
  • First Online:

Part of the book series: Contributions to Statistics ((CONTRIB.STAT.))

Abstract

The analysis of structural-change models is nowadays a popular subject of research both in econometric and statistical literature. The most challenging task is to identify multiple breaks occurring at unknown dates. In case of multiple shifts in mean Cappelli and Reale (Provasi, C. (eds.) S.Co. 2005: Modelli Complessi e Metodi Computazionali Intensivi per la Stima e la Previsione, pp. 479–484. Cleup, Padova, 2005) have proposed a method called ART that employs regression trees to estimate the number and location of breaks. In this paper we focus on regime changes due to breaks in the coefficients of a parametric model and we propose an extension of ART that addresses this topic in the general framework of the linear model with multiple structural changes. The proposed approach considers in the tree growing phase the residuals of parametric models fitted to contiguous subseries obtained by splitting the original series whereas tree pruning together with model selection criteria provides the number of breaks. We present simulation results well as two empirical applications pertaining to the behavior of the proposed approach.

This is a preview of subscription content, 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 EPUB and 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
Hardcover Book
USD   54.99
Price excludes VAT (USA)
  • Durable hardcover 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

Learn about institutional subscriptions

Notes

  1. 1.

    Note that estimation methods such as FM-OLS that allow for nonstationarity have not been considered due to the short sample size in the two sub-regimes.

References

  1. Andrews, D.W.K.: Tests for parameter instability ans structural change with unknown change point. Econometrica 61, 821–856 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  2. Apergis, N., Tsoumas, C.: A survey of the Feldstein Horioka puzzle: what has been done and where we stand. Res. Econ 63, 64–76 (2009)

    Article  Google Scholar 

  3. Bai, J.: Least square estimates of a shift in linear processes. J. Times Ser. Anal. 15, 453–472 (1994)

    Article  MATH  Google Scholar 

  4. Bai, J.: Estimating multiple breaks one at time. Economet. Theor. 15, 315–352 (1997)

    Article  Google Scholar 

  5. Bai, J., Perron, P.: Estimating and testing linear models with multiple structural changes. Econometrica 66, 47–78 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  6. Bai, J., Perron, P.: Computation and analysis of multiple structural change models. J. Appl. Economet. 18, 1–22 (2003)

    Article  Google Scholar 

  7. Bai, J., Perron, P.: Multiple structural change models: a simulation analysis. In: Broy, M., Dener, E. (eds.) Econometric Theory and Practice: Frontiers of Analysis and Applied Research, pp. 212–237. Cambridge University Press, Cambridge (2006)

    Chapter  Google Scholar 

  8. Banerjee, A., Urga, G.: Modelling structural breaks, long memory and stock market volatility: an overview. J. Economet. 129, 1–34 (2005)

    Article  MathSciNet  Google Scholar 

  9. Breiman, L., Friedman, J.H., Olshen, R.A., Stone, C.J.: Classification and Regression Trees. Wadsworth & Brooks, Monterey (CA) (1984)

    MATH  Google Scholar 

  10. Di Iorio, F., Fachin, S.: Savings and Investments in the OECD, 1970–2007: a Panel Cointegration test with breaks. MPRA Paper 3139, University Library of Munich, Germany (2010)

    Google Scholar 

  11. Cappelli, C., Di Iorio, F.: Structural breaks versus long memory: a simulation study. Stat. Appl. 17, 285–295 (2007)

    Google Scholar 

  12. Cappelli, C., Reale, M.: Dating multiple structural breaks occurring at unknown dates via Atheoretical Regression Trees. In: Provasi, C. (eds.) S.Co. 2005: Modelli Complessi e Metodi Computazionali Intensivi per la Stima e la Previsione, pp. 479–484. Cleup, Padova (2005)

    Google Scholar 

  13. Cappelli, C., Penny, R.N., Rea, W., Reale, M.: Detecting multiple mean breaks at unknown points with regression trees. Math. Comput. Simul. 78, 351–356 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  14. Chong, T.: Structural change in AR(1) models. Economet. Theor. 17, 87–155 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  15. Feldstein, M., Horioka, C.: Domestic saving and international capital flows. Econ. J. 90, 314–329 (1980)

    Article  Google Scholar 

  16. Granger, C.W.J., Hyung, J.: Occasional structural breaks and long memory with an application to the S&P 500 absolute stock returns. J. Emp. Fin. 11, 399–421 (2004)

    Article  Google Scholar 

  17. Hansen, B.: The new econometrics of structural change: dating breaks in U.S. labor productivity. J. Econ. Persp. 15, 117–128 (2001)

    Google Scholar 

  18. Hansen, B.: Testing for parameter instability in linear models. J. Policy Model. 14, 517–533 (1992)

    Article  Google Scholar 

  19. Pesaran, M.H., Pettenuzzo, D., Timmermann, A.G.: Forecasting time series subject to multiple structural breaks. Rev. Econ. Stud. 73, 1057–1084 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  20. Rea, W., Reale, M., Cappelli, C., Brown, J.A.: Identification of changes in mean with regression trees: an application to market research. Economet. Rev. 29, 754–777 (2010)

    Article  MathSciNet  Google Scholar 

  21. Smith, A.: Level shift and the illusion of long memory in economics time series. J. Bus. Econ. Stat. 23, 321–335 (2005)

    Article  Google Scholar 

  22. Su, X.G., Wang, M., Fan, J.J.: Maximum likelihood regression trees. J. Comput. Graph. Stat. 13, 586–598 (2004)

    Article  MathSciNet  Google Scholar 

  23. Zeiles, A., Kleiber, C., Kramer, W., Hornik, K.: Testing and dating of structural changes in practice. Comput. Stat. Data Anal. 44, 109–123 (2003)

    Article  Google Scholar 

Download references

Acknowledgements

Paper partially supported by MIUR grant (code 2008WKHJPK-PRIN2008-PUC number E61J10000020001)

Author information

Authors and Affiliations

  1. TEOMESUS, University Federico II, Naples, Italy

    Carmela Cappelli & Francesca Di Iorio

Authors
  1. Carmela Cappelli
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Francesca Di Iorio
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Carmela Cappelli .

Editor information

Editors and Affiliations

  1. , Statistical Sciences, University of Padua, Padua, Italy, Via Cesare Battisti 241, Padova, 35121, Italy

    Matteo Grigoletto

  2. , Statistical Sciences, University of Padua, Padua, Italy, Via Cesare Battisti 241, Padova, 35121, Italy

    Francesco Lisi

  3. , Dept of Decision Sciences, Bocconi University, Via Roentgen 1, Milano, 20123, Milano, Italy

    Sonia Petrone

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Italia

About this chapter

Cite this chapter

Cappelli, C., Iorio, F.D. (2013). Theoretical Regression Trees: A Tool for Multiple Structural-Change Models Analysis. In: Grigoletto, M., Lisi, F., Petrone, S. (eds) Complex Models and Computational Methods in Statistics. Contributions to Statistics. Springer, Milano. https://doi.org/10.1007/978-88-470-2871-5_6

Download citation

Publish with us

Policies and ethics

Search

Navigation