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Extreme Events – Charts sourced from Nematrian – Chapter 4

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Charts:

 

-          Figure 4.1: Illustrative principal components analysis

-          Figure 4.2: Schematic illustration of the impact of market dynamics

-          Figure 4.3: Fractile-fractile plot of blended PCA/ICA component rankings of sector relative returns showing number of observations in each fractile pairing, averaged across all principal component pairings and all +/- combinations of such pairs

-          Figure 4.4: Illustrative Gaussian mixture modelling analysis

-          Figure 4.5: Illustrative k-means clustering analysis

-          Figure 4.6: Illustration of the difficulties of finding global extrema, even in one dimension and even for smooth functions. Points A and C are local, but not global, maxima. The global maximum is at E, which is on the boundary of the interval so the derivative of the function need not vanish there. Points B and D are local minima and B is also the global minimum. The points F, G and H are said to bracket the maximum at A, since G is greater than both F and H and is in between them.

 


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