3D Scatter Plot from 20 February 2020 until 23 March 2020 (Turbulent Period) (IMAGE)
Caption
The difference between the average distance of normalized stock returns from two different periods can be used as an indicator to foresee a financially turbulent period by defining a threshold value to be used during normal periods since the average distance is higher during normal periods than during preceding and turbulent periods. Nonetheless, the issue with this approach is the fact that average distance of normalized stock returns suffers from the curse of dimensionality and fails to detect nonlinear and complex relationships in the data. The curse of dimensionality that average distance of normalized stock returns suffers is explained by the fact that as the number of dimensions (or stocks in this case) tends to infinity, the ratio between the distance of any points (say A and B), and the distance of any other points (say A and C) approaches 1. As a result, the average distance becomes meaningless. On the other hand, the implementation of PH information through WD or L^n norms of Persistent Landscape does not suffer from these issues. Hence, this is the reason for the success of the implementation of PH information in recent studies and its choice in this study.
Credit
Hugo Gobato Souto
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License
CC BY-NC-ND