image (5.22)

we have that by construction σ¯2=1Tt=1T(Rtμˆt|t1)2image, the sample variance of the data set. Such a restriction, called variance targeting, is often imposed in practical applications because it guarantees that, for a given data set, the ARCH(p) process will yield an unconditional variance that is exactly equal to the sample variance, which seems a sensible outcome. Note that this need stems from the common practice of estimating ARCH models using ML methods: under ML, the constrained optimization algorithm will aim at maximizing the probability ...

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