Skip to main content
SpringerLink
Log in

Regime dependent interconnectedness among fuzzy clusters of financial time series

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

Abstract

We analyze the dynamic structure of lower tail dependence coefficients within groups of assets defined such that assets belonging to the same group are characterized by pairwise high associations between extremely low values. The groups are identified by means of a fuzzy cluster analysis algorithm. The tail dependence coefficients are estimated using the Joe–Clayton copula function, and the 75th percentile within clusters is used as a measure of each cluster’s overall tail dependence. The interdependence structure of the clusters’ tail dependence dynamics is then analyzed in order to determine whether the pattern of a cluster can be predicted based on the past values of the others, using a Granger causality approach. The hypothesis of a possible regime switching dynamics in tail dependence is also investigated by means of a Threshold Vector AutoRegressive model and the results are compared to those obtained with a linear autoregression. The whole procedure is described with reference to a case study dealing with the assets composing Eurostoxx 50, but it can be viewed as the proposal of a general method, that can be relevantly applied to whatever set of asset returns time series.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

Notes

  1. The second step has been performed using the R package VineCopula (Schepsmeier et al. 2018).

  2. The cluster composition is supposed to be fixed in the rolling window analysis.

  3. There are other ways to compute joint membership degrees to clusters. We have verified that \(m_{h,t}^{(k)} = \min \left( m_i(k),m_j(k) \right) \) leads to very similar results in the terms of the final time series to be analyzed.

  4. We used the R package igraph (Csardi and Nepusz 2006).

References

  • Balla E, Ergen I, Migueis M (2014) Tail dependence and indicators of systemic risk for large us depositories. J Financ Stab 15:195–209

    Article  Google Scholar 

  • Billio M, Getmansky M, Lo AW, Pelizzon L (2012) Econometric measures of connectedness and systemic risk in the finance and insurance sectors. J Financ Econ 104(3):535–559

    Article  Google Scholar 

  • Campello RJ, Hruschka ER (2006) A fuzzy extension of the silhouette width criterion for cluster analysis. Fuzzy Sets Syst 157(21):2858–2875

    Article  MathSciNet  Google Scholar 

  • Csardi G, Nepusz T (2006) The igraph software package for complex network research. Int J Complex Syst 1695:1–19

    Google Scholar 

  • De Luca G, Zuccolotto P (2011) A tail dependence-based dissimilarity measure for financial time series clustering. Adv Data Anal Classif 5(4):323–340

    Article  MathSciNet  Google Scholar 

  • De Luca G, Zuccolotto P (2015) Dynamic tail dependence clustering of financial time series. Stat Pap 58:1–17

    MathSciNet  MATH  Google Scholar 

  • De Luca G, Zuccolotto P (2017) A double clustering algorithm for financial time series based on extreme events. Stat Risk Model 34:1–12

    Article  MathSciNet  Google Scholar 

  • Di Narzo AF, Aznarte JL, Stigler M, Tsung-Wu H (2020) tsDyn: nonlinear time series models with regime switching. https://cran.r-project.org/web/packages/tsDyn/

  • Disegna M, D’Urso P, Durante F (2017) Copula-based fuzzy clustering of spatial time series. Spat Stat 21:209–225

    Article  MathSciNet  Google Scholar 

  • Durante F, Pappadà R, Torelli N (2014) Clustering of financial time series in risky scenarios. Adv Data Anal Classif 8(4):359–376

    Article  MathSciNet  Google Scholar 

  • Durante F, Pappadà R, Torelli N (2015) Clustering of time series via non-parametric tail dependence estimation. Stat Pap 56(3):701–721

    Article  MathSciNet  Google Scholar 

  • D’Urso P, Cappelli C, Di Lallo D, Massari R (2013) Clustering of financial time series. Phys A Stat Mech Appl 392(9):2114–2129

    Article  MathSciNet  Google Scholar 

  • D’Urso P, De Giovanni L, Massari R (2016) Garch-based robust clustering of time series. Fuzzy Sets Syst 305:1–28

    Article  MathSciNet  Google Scholar 

  • D’Urso P, De Giovanni L, Massari R (2019) Trimmed fuzzy clustering of financial time series based on dynamic time warping. Ann Oper Res 2019:1–17

    Google Scholar 

  • Ferraro M, Giordani P, Serafini A (2019) Fclust: an R package for fuzzy clustering. The R Journal 11. https://journal.r-project.org/archive/2019/RJ-2019-017/RJ-2019-017.pdf

  • Hansen BE (1999) Testing for linearity. J Econ Surv 13(5):551–576

    Article  Google Scholar 

  • Hubrich K, Teräsvirta T (2013) Thresholds and smooth transitions in vector autoregressive models. Adv Econom 32:273–326

    Article  MathSciNet  Google Scholar 

  • Joe H (1997) Multivariate models and multivariate dependence concepts. CRC Press, Boca Raton

    Book  Google Scholar 

  • Joe H (2005) Asymptotic efficiency of the two-stage estimation method for copula-based models. J Multivar Anal 94:401–419

    Article  MathSciNet  Google Scholar 

  • Lafuente-Rego B, Vilar JA (2016) Clustering of time series using quantile autocovariances. Adv Data Anal Classif 10(3):391–415

    Article  MathSciNet  Google Scholar 

  • Lafuente-Rego B, D’Urso P, Vilar JA (2018) Robust fuzzy clustering based on quantile autocovariances. Stat Pap 2018:1–56

    MATH  Google Scholar 

  • Liu X, Wu J, Yang C, Jiang W (2018) A maximal tail dependence-based clustering procedure for financial time series and its applications in portfolio selection. Risks 6(115):1–26

    Google Scholar 

  • Lo MC, Zivot E (2001) Threshold cointegration and nonlinear adjustment to the law of one price. Macroecon Dyn 5:533–576

    Article  Google Scholar 

  • Patro DK, Qi M, Sun X (2013) A simple indicator of systemic risk. J Financ Stab 9(1):105–116

    Article  Google Scholar 

  • Ruspini EH (1969) A new approach to clustering. Inf Control 15(1):22–32

    Article  Google Scholar 

  • Ruspini EH, Bezdek JC, Keller JM (2019) Fuzzy clustering: a historical perspective. IEEE Comput Intell Mag 14(1):45–55

    Article  Google Scholar 

  • Schepsmeier U, Stoeber J, Brechmann EC, Graeler B, Nagler T, Erhardt T (2018) VineCopula: statistical inference of vine copulas. R package version 2.1.8. Available on CRAN

  • Sims C (1980) Macroeconomics and reality. Econometrica 48:1–48

    Article  Google Scholar 

  • Vilar JA, Lafuente-Rego B, D’Urso P (2017) Quantile autocovariances: a powerful tool for hard and soft partitional clustering of time series. Fuzzy Sets Syst 340:38–72

    Article  MathSciNet  Google Scholar 

  • Winkler R, Klawonn F, Kruse R (2011) Fuzzy clustering with polynomial fuzzifier function in connection with m-estimators. Appl Comput Math 10(1):146–163

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Naples Parthenope, Via G. Parisi, 13, 80132, Naples, Italy

    Giovanni De Luca

  2. University of Brescia, C.da S. Chiara 50, 25122, Brescia, Italy

    Paola Zuccolotto

Authors
  1. Giovanni De Luca
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Paola Zuccolotto
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Giovanni De Luca.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

De Luca, G., Zuccolotto, P. Regime dependent interconnectedness among fuzzy clusters of financial time series. Adv Data Anal Classif 15, 315–336 (2021). https://doi.org/10.1007/s11634-020-00405-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11634-020-00405-8

Keywords

Mathematics Subject Classification

Search

Navigation