  Portfolio allocation and risk management make use of correlation matrices and
heavily rely on the choice of a proper correlation matrix to be used. In this
regard, one important question is related to the choice of the proper sample
period to be used to estimate a stable correlation matrix. This paper addresses
this question and proposes a new methodology to estimate the correlation matrix
which doesn't depend on the chosen sample period. This new methodology is based
on tensor factorization techniques. In particular, combining and normalizing
factor components, we build a correlation matrix which shows emerging
structural dependency properties not affected by the sample period. To retrieve
the factor components, we propose a new tensor decomposition (which we name
Slice-Diagonal Tensor (SDT) factorization) and compare it to the two most used
tensor decompositions, the Tucker and the PARAFAC. We have that the new
factorization is more parsimonious than the Tucker decomposition and more
flexible than the PARAFAC. Moreover, this methodology applied to both simulated
and empirical data shows results which are robust to two non-parametric tests,
namely Kruskal-Wallis and Kolmogorov-Smirnov tests. Since the resulting
correlation matrix features stability and emerging structural dependency
properties, it can be used as alternative to other correlation matrices type of
measures, including the Person correlation.
