  Stock market returns are typically analyzed using standard regression, yet
they reside on irregular domains which is a natural scenario for graph signal
processing. To this end, we consider a market graph as an intuitive way to
represent the relationships between financial assets. Traditional methods for
estimating asset-return covariance operate under the assumption of statistical
time-invariance, and are thus unable to appropriately infer the underlying true
structure of the market graph. This work introduces a class of graph spectral
estimators which cater for the nonstationarity inherent to asset price
movements, and serve as a basis to represent the time-varying interactions
between assets through a dynamic spectral market graph. Such an account of the
time-varying nature of the asset-return covariance allows us to introduce the
notion of dynamic spectral portfolio cuts, whereby the graph is partitioned
into time-evolving clusters, allowing for online and robust asset allocation.
The advantages of the proposed framework over traditional methods are
demonstrated through numerical case studies using real-world price data.
