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Regime dependent interconnectedness among fuzzy clusters of financial time series. (English) Zbl 07363876

Summary: 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.

MSC:

62H30 Classification and discrimination; cluster analysis (statistical aspects)
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
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[1] Balla, E.; Ergen, I.; Migueis, M., Tail dependence and indicators of systemic risk for large us depositories, J Financ Stab, 15, 195-209 (2014) · doi:10.1016/j.jfs.2014.10.002
[2] Billio, M.; Getmansky, M.; Lo, AW; Pelizzon, L., Econometric measures of connectedness and systemic risk in the finance and insurance sectors, J Financ Econ, 104, 3, 535-559 (2012) · doi:10.1016/j.jfineco.2011.12.010
[3] Campello, RJ; Hruschka, ER, A fuzzy extension of the silhouette width criterion for cluster analysis, Fuzzy Sets Syst, 157, 21, 2858-2875 (2006) · Zbl 1103.68674 · doi:10.1016/j.fss.2006.07.006
[4] Csardi, G.; Nepusz, T., The igraph software package for complex network research, Int J Complex Syst, 1695, 1-19 (2006)
[5] De Luca, G.; Zuccolotto, P., A tail dependence-based dissimilarity measure for financial time series clustering, Adv Data Anal Classif, 5, 4, 323-340 (2011) · doi:10.1007/s11634-011-0098-3
[6] De Luca, G.; Zuccolotto, P., Dynamic tail dependence clustering of financial time series, Stat Pap, 58, 1-17 (2015) · Zbl 1416.62581
[7] De Luca, G.; Zuccolotto, P., A double clustering algorithm for financial time series based on extreme events, Stat Risk Model, 34, 1-12 (2017) · Zbl 1362.60051 · doi:10.1515/strm-2015-0026
[8] 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/
[9] Disegna, M.; D’Urso, P.; Durante, F., Copula-based fuzzy clustering of spatial time series, Spat Stat, 21, 209-225 (2017) · doi:10.1016/j.spasta.2017.07.002
[10] Durante, F.; Pappadà, R.; Torelli, N., Clustering of financial time series in risky scenarios, Adv Data Anal Classif, 8, 4, 359-376 (2014) · Zbl 1414.62241 · doi:10.1007/s11634-013-0160-4
[11] Durante, F.; Pappadà, R.; Torelli, N., Clustering of time series via non-parametric tail dependence estimation, Stat Pap, 56, 3, 701-721 (2015) · Zbl 1317.62053 · doi:10.1007/s00362-014-0605-7
[12] D’Urso, P.; Cappelli, C.; Di Lallo, D.; Massari, R., Clustering of financial time series, Phys A Stat Mech Appl, 392, 9, 2114-2129 (2013) · doi:10.1016/j.physa.2013.01.027
[13] D’Urso, P.; De Giovanni, L.; Massari, R., Garch-based robust clustering of time series, Fuzzy Sets Syst, 305, 1-28 (2016) · Zbl 1368.62167 · doi:10.1016/j.fss.2016.01.010
[14] D’Urso, P.; De Giovanni, L.; Massari, R., Trimmed fuzzy clustering of financial time series based on dynamic time warping, Ann Oper Res, 2019, 1-17 (2019)
[15] 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
[16] Hansen, BE, Testing for linearity, J Econ Surv, 13, 5, 551-576 (1999) · doi:10.1111/1467-6419.00098
[17] Hubrich, K.; Teräsvirta, T., Thresholds and smooth transitions in vector autoregressive models, Adv Econom, 32, 273-326 (2013) · Zbl 1443.62153 · doi:10.1108/S0731-9053(2013)0000031008
[18] Joe, H., Multivariate models and multivariate dependence concepts (1997), Boca Raton: CRC Press, Boca Raton · Zbl 0990.62517 · doi:10.1201/b13150
[19] Joe, H., Asymptotic efficiency of the two-stage estimation method for copula-based models, J Multivar Anal, 94, 401-419 (2005) · Zbl 1066.62061 · doi:10.1016/j.jmva.2004.06.003
[20] Lafuente-Rego, B.; Vilar, JA, Clustering of time series using quantile autocovariances, Adv Data Anal Classif, 10, 3, 391-415 (2016) · Zbl 1414.62372 · doi:10.1007/s11634-015-0208-8
[21] Lafuente-Rego, B.; D’Urso, P.; Vilar, JA, Robust fuzzy clustering based on quantile autocovariances, Stat Pap, 2018, 1-56 (2018) · Zbl 1397.62233
[22] Liu, X.; Wu, J.; Yang, C.; Jiang, W., A maximal tail dependence-based clustering procedure for financial time series and its applications in portfolio selection, Risks, 6, 115, 1-26 (2018)
[23] Lo, MC; Zivot, E., Threshold cointegration and nonlinear adjustment to the law of one price, Macroecon Dyn, 5, 533-576 (2001) · Zbl 1008.91504 · doi:10.1017/S1365100501023057
[24] Patro, DK; Qi, M.; Sun, X., A simple indicator of systemic risk, J Financ Stab, 9, 1, 105-116 (2013) · doi:10.1016/j.jfs.2012.03.002
[25] Ruspini, EH, A new approach to clustering, Inf Control, 15, 1, 22-32 (1969) · Zbl 0192.57101 · doi:10.1016/S0019-9958(69)90591-9
[26] Ruspini, EH; Bezdek, JC; Keller, JM, Fuzzy clustering: a historical perspective, IEEE Comput Intell Mag, 14, 1, 45-55 (2019) · doi:10.1109/MCI.2018.2881643
[27] 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
[28] Sims, C., Macroeconomics and reality, Econometrica, 48, 1-48 (1980) · doi:10.2307/1912017
[29] Vilar, JA; Lafuente-Rego, B.; D’Urso, P., Quantile autocovariances: a powerful tool for hard and soft partitional clustering of time series, Fuzzy Sets Syst, 340, 38-72 (2017) · Zbl 1397.62233 · doi:10.1016/j.fss.2017.03.006
[30] Winkler, R.; Klawonn, F.; Kruse, R., Fuzzy clustering with polynomial fuzzifier function in connection with m-estimators, Appl Comput Math, 10, 1, 146-163 (2011) · Zbl 1208.62105
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