Given a matrix that contains row-wise the assets' returns and a sliding window
win_length, this function computes an approximation of the joint distribution (copula, e.g. see https://en.wikipedia.org/wiki/Copula_(probability_theory)) between portfolios' return and volatility in each time period defined by
For each copula it computes an indicator: If the indicator is large it corresponds to a crisis period and if it is small it corresponds to a normal period.
In particular, the periods over which the indicator is greater than 1 for more than 60 consecutive sliding windows are warnings and for more than 100 are crisis. The sliding window is shifted by one day.
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A d-dimensional vector that describes the direction of the first family of parallel hyperplanes.
A list to set a parameterization.
A list that contains the indicators and the corresponding vector that label each time period with respect to the market state: a) normal, b) crisis, c) warning.
L. Cales, A. Chalkis, I.Z. Emiris, V. Fisikopoulos, “Practical volume computation of structured convex bodies, and an application to modeling portfolio dependencies and financial crises,” Proc. of Symposium on Computational Geometry, Budapest, Hungary, 2018.
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