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6028统计困难derivationlong

Fat Tails: Unconditional Kurtosis of GARCH Returns

题目

Let rt=htztr_t=\sqrt{h_t}\,z_t with ztN(0,1)z_t\sim N(0,1) i.i.d. and GARCH(1,1) variance. The unconditional kurtosis (when finite) is K=3[1(α+β)2]1(α+β)22α2K=\dfrac{3\,[1-(\alpha+\beta)^2]}{1-(\alpha+\beta)^2-2\alpha^2}. For α=0.1\alpha=0.1, β=0.85\beta=0.85, compute KK and state whether returns are leptokurtic. Give KK as a decimal.

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K

leptokurtic