GARCH-based robust clustering of time series

Abstract

In this paper we propose different robust fuzzy clustering models for classifying heteroskedastic (volatility) time series, following the so-called model-based approach to time series clustering and using a partitioning around medoids procedure. The proposed models are based on a GARCH parametric modelingof the time series, i.e. the unconditional volatility and the time-varying volatility GARCH representation of the time series. We first suggest a timid robustification of the fuzzy clustering. Then, we propose three robust fuzzy clustering models belonging to the so-called metric, noise and trimmed approaches, respectively. Each model neutralizes the negative effects of the outliers in the clustering process in a different manner. In particular, the first robust model, based on the metric approach, achieves its robustness with respect to outliers by taking into account a “robust” distance measure; the second, based on the noise approach, achieves its robustness by introducing a noise cluster represented by a noise prototype; the third, based on the trimmed approach, achieves its robustness by trimming away a certain fraction of outlying time series. The usefulness and effectiveness of the proposed clustering models is illustrated by means of a simulation study and two applications in finance and economics

Robust multivariate and functional archetypal analysis with application to financial time series analysis

“…AA has also been applied in market research (Li et al (2003); Porzio et al (2008); Midgley and Venaik (2013)) in the multivariate context. Despite the fact that financial time series are commonly analyzed by unsupervised techniques ranging from PCA (Alexander (2001); Tsay (2010); Ingrassia and Costanzo (2005)) to clustering (Dose and Cincotti (2005); Basalto et al (2007); Tseng and Li (2012);D'Urso et al (2013); Dias et al (2015); Ann Ma-haraj et al (2010); Cappelli et al (2013);D'Urso et al (2014); D'Urso and Maharaj (2012);D'Urso (2004D'Urso ( , 2005; Alonso and Peña (2018)), including robust versions of these (Malioutov (2013); Verdonck et al (2011);D'Urso et al (2016D'Urso et al ( , 2018), to the best of our knowledge functional archetypal analysis has not been used in financial or business applications until now.…”

Enhancement of SVC performance in electric arc furnace for flicker suppression using a Gray‐ANN based prediction method

“…Unlike the numeric TLF which implements deterministic load flow for all the time samples, the analytic TLF is implemented only once for the entire time. Different robust fuzzy clustering models for classifying heteroskedastic time series have been proposed in the previous study . The proposed models are based on a GARCH parametric modeling of the time series.…”

“…Different robust fuzzy clustering models for classifying heteroskedastic time series have been proposed in the previous study. 30 The proposed models are based on a GARCH parametric modeling of the time series. An innovative tuning approach for fuzzy control systems with a reduced parametric sensitivity using the Gray Wolf Optimizer algorithm has been proposed in the previous study.…”

Copula-based fuzzy clustering of spatial time series

“…Following Caiado et al (2015) time series clustering methods can be classified into three methodological approaches (for more details, see also Warren Liao, 2005;Caiado et al, 2015;D'Urso et al, 2016a):…”

“…• GARCH representation (see, e.g., Caiado & Crato, 2010;Otranto, 2010;D'Urso et al, 2013aD'Urso et al, , 2016a);…”