Clustering Heteroskedastic Time Series by Model-Based Procedures

Financial time series are often characterized by similar volatility structures, often represented by GARCH processes. The detection of clusters of series displaying similar behavior could be important to understand the differences in the estimated processes, without having to study and compare the estimated parameters across all the series. This is particularly relevant dealing with many series, as in ?nancial applications. The volatility of a time series can be characterized in terms of the underlying GARCH process. Using Wald tests and the AR metrics to measure the distance between GARCH processes, it is possible to develop a clustering algorithm, which can provide three classi?cations (with increasing degree of deepness) based on the heteroskedastic patterns of the time series. The number of clusters is detected automatically and it is not ?xed a priori or a posteriori. The procedure is evaluated by simulations and applied to the sector indexes of the Italian market.