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How misleading can sample ACFs of stable MAs be? (Very!). (English) Zbl 0959.62076
Summary: For the stable moving average process \[ X_t=\int^\infty_{-\infty}f(t+x)M(dx),\;t=1,2,\dots, \] we find the weak limit of its sample autocorrelation function as the sample size \(n\) increases to \(\infty\). It turns out that, as a rule, this limit is random! This shows how dangerous it is to rely on sample correlation as a model fitting tool in the heavy tailed case. We discuss for what functions \(f\) this limit is nonrandom for all (or only some – this can be the case, too!) lags.

MSC:
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62G32 Statistics of extreme values; tail inference
60E07 Infinitely divisible distributions; stable distributions
60G70 Extreme value theory; extremal stochastic processes
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