Extreme events: blending PCA and ICA [23]

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Bullet points include: Both PCA and ICA assume that observations are (time stationary) linear combination mixtures. i.e. a = a1q1 + ... + anqn  and y = Wx . But not all mixtures are of this form. Consider distributional mixtures, y drawn from distribution D1 with probability p1, from distribution D2 with probability p2 etc. These typically result in fat-tailed behaviour. Very important special case is modelling a time-varying world. c.f. GARCH, regime shifts etc. Also, Cornish-Fisher (and hence kurtosis) may misestimate sizes of fat tails

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