Skip to main content

Comparing Multistep Ahead Forecasting Functions for Time Series Clustering

  • Conference paper
  • First Online:
Classification, (Big) Data Analysis and Statistical Learning

Abstract

The autoregressive metric between ARIMA processes has been originally introduced as the Euclidean distance between the AR weights of the one-step-ahead forecasting functions. This article proposes a novel distance criterion between time series that compares the corresponding multistep ahead forecasting functions and that relies on the direct method for model estimation. The proposed approach is complemented by a strategy for visual exploration and clustering based on the DISTATIS algorithm.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 89.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 119.99
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

References

  1. Abdi, H., Valentin, D., O’Toole, A.J. Edelman, B.; DISTATIS: the analysis of multiple distance matrices. Proc.IEEE Computer Society: Computer Vision and Pattern Recognition, IEEE Computer Society, 42–47 (2005)

    Google Scholar 

  2. Abdi, H., Williams, L.J., Valentin, D., Bennani-Dosse, M.: STATIS and DISTATIS: optimum multitable principal component analysis and three way metric multidimensional scaling. Wiley Interdisc. Rev. Comput. Stat. 4(2), 124–167 (2012)

    Article  Google Scholar 

  3. Bhansali, R.J.: Asymptotically efficient autoregressive model selection for multistep prediction. Ann. Inst. Stat. Math. 48, 577–602 (1996)

    Article  MathSciNet  Google Scholar 

  4. Carroll, J.D., Chang, J.J.: Analysis of individual differences in multidimensional scaling via an n-way generalization of Eckart-Young decomposition. Psychometrika 35, 283–319 (1970)

    Article  Google Scholar 

  5. Chevillon, G.: Direct multi-step estimation and forecasting. J. Econ. Surv. 21, 746–785 (2007)

    Article  Google Scholar 

  6. Clements, M.P., Hendry, D.F.: Multi-step estimation for forecasting. Oxf. Bull. Econ. Stat. 58, 657–684 (1996)

    Article  Google Scholar 

  7. Corduas, M.: La metrica autoregressiva tra modelli ARIMA: una procedura in linguaggio GAUSS. Quad. di stat. 2, 1–37 (2000)

    Google Scholar 

  8. Corduas, M.: Clustering streamflow time series for regional classification. J. Hydrol. 407, 73–80 (2011)

    Article  Google Scholar 

  9. Corduas, M., Piccolo, D.: Time series clustering and classification by the autoregressive metric. Comput. Stat. Data Anal. 52, 1860–1862 (2008)

    Article  MathSciNet  Google Scholar 

  10. Cox, T.F., Cox, M.A.: Multidimensional scaling. Chapman & Hall-CRC Press, Boca Raton (2000)

    MATH  Google Scholar 

  11. Di Iorio, F., Triacca, U.: Testing for Granger non-causality using the autoregressive metric. Econ. Modell. 33, 120–125 (2013)

    Google Scholar 

  12. Findley, D.F.: On the use of multiple models for multi-period forecasting. In: Proceedings of Business and Economic Statistics, American Statistical Association, pp. 528–531 (1983)

    Google Scholar 

  13. Husson, F., Pagès, J.: INDSCAL model: geometrical interpretation and methodology. Comput. stat. Data Anal. 50, 358–378 (2006)

    Google Scholar 

  14. Otranto, E.: Clustering heteroskedastic time series by model-based procedures. Comput. Stat. Data Anal. 52, 4685–4698 (2008)

    Article  MathSciNet  Google Scholar 

  15. Otranto, E.: Identifying financial time series with similar dynamic conditional correlation. Comput. Stat. Data Anal. 54, 1–15 (2010)

    Article  MathSciNet  Google Scholar 

  16. Palomba, G., Sarno, E., Zazzaro, A.: Testing similarities of short-run inflation dynamics among EU-25 countries after the Euro. Empirical Econ. 37, 231–270 (2009)

    Article  Google Scholar 

  17. Piccolo, D.: A distance measure for classifying ARIMA models. J. Time Ser. Anal. 11, 153–164 (1990)

    Article  Google Scholar 

  18. Tiao, G.C., Tsay, R.S.: Some advances in non-linear and adaptive modelling in time-series. J. Forecast. 13, 109–131 (1994)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Marcella Corduas .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Corduas, M., Ragozini, G. (2018). Comparing Multistep Ahead Forecasting Functions for Time Series Clustering. In: Mola, F., Conversano, C., Vichi, M. (eds) Classification, (Big) Data Analysis and Statistical Learning. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Cham. https://doi.org/10.1007/978-3-319-55708-3_21

Download citation

Publish with us

Policies and ethics