I have been given time series of N stock prices and time series of K sectoral indices. (Sectoral index is index made from all stocks belonging to that sector.) I have not been given names of any of those stocks or indices. I want to know which stocks belong to the same sector and sectoral indices. I am able to cluster the stocks. But how should I decide which sectoral index time series they correspond to? Should I just cluster stocks and indices together (N+K timeseries) instead of clustering N stocks independently? Will that be correct approach?
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