Clustering Heteroskedastic Time Series by Model-Based Procedures

Financial time series are often characterized by similar volatility structures. The detection
of clusters of series displaying similar behavior could be important in understanding the
differences in the estimated processes, without having to study and compare the estimated
parameters across all the series. This is particularly relevant when dealing with many
series, as in financial applications. The volatility of a time series can be characterized in
terms of the underlying GARCH process. Using Wald tests and the Autoregressive metrics
to measure the distance between GARCH processes, it is shown that it is possible to develop
a clustering algorithm, which can provide three classifications (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 fixed a priori or a posteriori. The procedure
is evaluated by simulations and applied to the sector indices of the Italian market.