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.

GARCH-based robust clustering of time series / DE GIOVANNI, Livia; D'Urso, Pierpaolo; Massari, Riccardo. - In: FUZZY SETS AND SYSTEMS. - ISSN 0165-0114. - 305:(2016), pp. 1-28. [10.1016/j.fss.2016.01.010]

GARCH-based robust clustering of time series

DE GIOVANNI, LIVIA;
2016

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.
Heteroskedastic time series; Unconditional and time-varying volatility; GARCH model; Fuzzy partitioning around medoids; Outliers; Robust metric; Noise cluster; Trimming; Volatilities daily stocks returns; International stock-market volatility daily returns
GARCH-based robust clustering of time series / DE GIOVANNI, Livia; D'Urso, Pierpaolo; Massari, Riccardo. - In: FUZZY SETS AND SYSTEMS. - ISSN 0165-0114. - 305:(2016), pp. 1-28. [10.1016/j.fss.2016.01.010]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11385/164603
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