  We study soft persistence (existence in subsequent temporal layers of motifs
from the initial layer) of motif structures in Triangulated Maximally Filtered
Graphs (TMFG) generated from time-varying Kendall correlation matrices computed
from stock prices log-returns over rolling windows with exponential smoothing.
We observe long-memory processes in these structures in the form of power law
decays in the number of persistent motifs. The decays then transition to a
plateau regime with a power-law decay with smaller exponent. We demonstrate
that identifying persistent motifs allows for forecasting and applications to
portfolio diversification. Balanced portfolios are often constructed from the
analysis of historic correlations, however not all past correlations are
persistently reflected into the future. Sector neutrality has also been a
central theme in portfolio diversification and systemic risk. We present an
unsupervised technique to identify persistently correlated sets of stocks.
These are empirically found to identify sectors driven by strong fundamentals.
Applications of these findings are tested in two distinct ways on four
different markets, resulting in significant reduction in portfolio volatility.
A persistence-based measure for portfolio allocation is proposed and shown to
outperform volatility weighting when tested out of sample.
