  The inference of causal structures from observed data plays a key role in
unveiling the underlying dynamics of the system. This paper exposes a novel
method, named Multiscale-Causal Structure Learning (MS-CASTLE), to estimate the
structure of linear causal relationships occurring at different time scales.
Differently from existing approaches, MS-CASTLE takes explicitly into account
instantaneous and lagged inter-relations between multiple time series,
represented at different scales, hinging on stationary wavelet transform and
non-convex optimization. MS-CASTLE incorporates, as a special case, a
single-scale version named SS-CASTLE, which compares favorably in terms of
computational efficiency, performance and robustness with respect to the state
of the art onto synthetic data. We used MS-CASTLE to study the multiscale
causal structure of the risk of 15 global equity markets, during covid-19
pandemic, illustrating how MS-CASTLE can extract meaningful information thanks
to its multiscale analysis, outperforming SS-CASTLE. We found that the most
persistent and strongest interactions occur at mid-term time resolutions.
Moreover, we identified the stock markets that drive the risk during the
considered period: Brazil, Canada and Italy. The proposed approach can be
exploited by financial investors who, depending to their investment horizon,
can manage the risk within equity portfolios from a causal perspective.
