Source: Adv. in Appl. Probab.
Volume 42, Number 1
For a time series, a plot of sample covariances is a popular way to assess its
dependence properties. In this paper we give a systematic characterization of
the asymptotic behavior of sample covariances of long-memory linear processes.
Central and noncentral limit theorems are obtained for sample covariances with
bounded as well as unbounded lags. It is shown that the limiting distribution
depends in a very interesting way on the strength of dependence, the
heavy-tailedness of the innovations, and the magnitude of the lags.
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