## A fragmented-periodogram approach for clustering big data time series.(English)Zbl 1474.62214

Summary: We propose and study a new frequency-domain procedure for characterizing and comparing large sets of long time series. Instead of using all the information available from data, which would be computationally very expensive, we propose some regularization rules in order to select and summarize the most relevant information for clustering purposes. Essentially, we suggest to use a fragmented periodogram computed around the driving cyclical components of interest and to compare the various estimates. This procedure is computationally simple, but able to condense relevant information of the time series. A simulation exercise shows that the smoothed fragmented periodogram works in general better than the non-smoothed one and not worse than the complete periodogram for medium to large sample sizes. We illustrate this procedure in a study of the evolution of several stock markets indices. We further show the effect of recent financial crises over these indices behaviour.

### MSC:

 62H30 Classification and discrimination; cluster analysis (statistical aspects) 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 62M15 Inference from stochastic processes and spectral analysis 62R07 Statistical aspects of big data and data science 62P05 Applications of statistics to actuarial sciences and financial mathematics
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