Theorems and fallacies in the theory of long-range-dependent Processes

@article{Gubner2005TheoremsAF,
  title={Theorems and fallacies in the theory of long-range-dependent Processes},
  author={John A. Gubner},
  journal={IEEE Transactions on Information Theory},
  year={2005},
  volume={51},
  pages={1234-1239}
}
It is frequently claimed in the literature that long-range dependence has equivalent formulations in the time domain and the frequency domain. Although many researchers understand that this is only "operationally true," i.e., it holds in cases of interest, many state this equivalence as a mathematical theorem. In particular, it is claimed as a theorem in the literature that if a covariance function decays like one over a fractional power of n, then the corresponding power spectral density tends… CONTINUE READING
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