  We introduce a new factor model for log volatilities that performs
dimensionality reduction and considers contributions globally through the
market, and locally through cluster structure and their interactions. We do not
assume a-priori the number of clusters in the data, instead using the Directed
Bubble Hierarchical Tree (DBHT) algorithm to fix the number of factors. We use
the factor model and a new integrated non parametric proxy to study how
volatilities contribute to volatility clustering. Globally, only the market
contributes to the volatility clustering. Locally for some clusters, the
cluster itself contributes statistically to volatility clustering. This is
significantly advantageous over other factor models, since the factors can be
chosen statistically, whilst also keeping economically relevant factors.
Finally, we show that the log volatility factor model explains a similar amount
of memory to a Principal Components Analysis (PCA) factor model and an
exploratory factor model.
