The forward search interactive outlier detection in cointegrated VAR analysis | Advances in Data Analysis and Classification
Skip to main content
Springer Nature Link
Log in

The forward search interactive outlier detection in cointegrated VAR analysis

  • Regular Article
  • Published:
Advances in Data Analysis and Classification Aims and scope Submit manuscript

Abstract

Cointegration analysis is particularly sensitive to outlying observations. Traditional robust approaches rely on parameter estimates based on weighting schemes to penalize aberrant units. This, in particular, is the idea underlying pseudo maximum likelihood robust estimators. Atypical observations, however, can reveal useful information about the investigated phenomenon. Aiming to detect these observations, we extend the forward search procedure to the cointegrated vector autoregressive model. The analysis is carried out by building up subsets of increasing dimension and monitoring suitable statistics at each subset size. Simulation experiments and real data analysis highlight that our forward search is more effective than the pseudo maximum likelihood in detecting atypical units and data structures.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
¥17,985 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Japan)

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

Notes

  1. It is worth mentioning that the symbol \({}^*\) relates to the parameter vector associated to the optimal subset (of size m) and not to the size of the subset.

References

  • Atkinson AC, Riani M (2000) Robust diagnostic regression analysis. Springer, New York

    Book  MATH  Google Scholar 

  • Atkinson AC, Riani M (2006) Distribution theory and simulations for tests of outliers in regression. J Comput Gr Stat 15:460–476

    Article  MathSciNet  Google Scholar 

  • Atkinson AC, Riani M, Cerioli A (2004) Exploring multivariate data with the forward search. Springer, New York

    Book  MATH  Google Scholar 

  • Bellini T, Riani M (2012) Robust analysis of default intensity. Comput Stat Data Ana 56(11):3276–3285

    Article  MathSciNet  MATH  Google Scholar 

  • Bosco B, Parisio L, Pelagatti M, Baldi F (2010) Long-run relations in European electricity prices. J Appl Econom 25:805–832

    Article  MathSciNet  Google Scholar 

  • Campbell JY, Perron P (1991) Pitfalls and opportunities: What macroeconomists should know about unit roots. In: NBER macroeconomic annual. National Bureau of Economic Research, Cambridge, pp 141–218

  • Franses PH, Haldrup N (1994) The effects of additive outliers on tests for unit roots and cointegration. J Bus Econ Stat 12:471–478

    MathSciNet  Google Scholar 

  • Franses PH, Lucas A (1998) Outlier detection in cointegration analysis. J Bus Econ Stat 16:459–468

    Google Scholar 

  • Franses PH, Kloek T, Lucas A (1998) Outlier robust analysis of long-run marketing effects for weekly scanning data. J Econom 89:293–315

    Article  MATH  Google Scholar 

  • Johansen S (1988) Statistical analysis of cointegration vectors. J Econ Dyn Control 12:231–254

    Article  MathSciNet  MATH  Google Scholar 

  • Johansen S (1991) Estimation and hypothesis testing of cointegration vectors in Gaussian vector autoregressive models. Econometrica 59:1551–1580

    Article  MathSciNet  MATH  Google Scholar 

  • Johansen S (1996) Likelihood-based inference in cointegrated vector autoregressive models. Oxford University Press, Oxford

    MATH  Google Scholar 

  • Johansen S, Nielsen B (2010) Discussion: the forward search: theory and data analysis. J Korean Stat Soc 39:137–145

    Article  MathSciNet  MATH  Google Scholar 

  • Johansen S, Nielsen B (2015) Analysis of the forward search using some new results for martingales and empirical processes. Bernoulli J (forthcoming)

  • Johansen S, Mosconi R, Nielsen B (2000) Cointegration analysis in the presence of structural breaks in the deterministic trend. Econom J 3:216–249

    Article  MathSciNet  MATH  Google Scholar 

  • Lucas A (1995) An outlier robust unit root test with an application to the extended Nelson–Plosser data. J Econom 66:153–174

    Article  MATH  Google Scholar 

  • Lucas A (1997) Cointegration testing using pseudolikelihood ratio tests. Econom Theory 13:149–169

    Article  MathSciNet  Google Scholar 

  • Nielsen HB (2004) Cointegration analysis in the presence of outliers. Econom J 7:249–271

    Article  MathSciNet  MATH  Google Scholar 

  • Riani M, Atkinson AC, Cerioli A (2009) Finding an unknown number of multivariate outliers. J R Stat Soc Ser B 71:201–221

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

I am very grateful to the Editor and two anonymous referees for very constructive suggestions. I also thank Marco Riani, Søren Johansen, Bent Nielsen, Matteo Pelagatti and Daniel Ruediger for valuable comments on earlier drafts.

Author information

Authors and Affiliations

  1. Università degli Studi di Parma, Parma, Italy

    Tiziano Bellini

Authors
  1. Tiziano Bellini
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tiziano Bellini.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bellini, T. The forward search interactive outlier detection in cointegrated VAR analysis. Adv Data Anal Classif 10, 351–373 (2016). https://doi.org/10.1007/s11634-015-0216-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11634-015-0216-8

Keywords

Mathematics Subject Classification

Search

Navigation