Long range dependence for stable random processes - Vitalii Makogin; Marco Oesting; Albert Rapp; Evgeny Spodarev (Journal of Time Series Analysis, 2021)
We investigate long and short memory in α-stable moving averages and max-stable processes with α-Fréchet marginal distributions. As these processes are heavy-tailed, we rely on the notion of long range dependence based on the covariance of indicators of excursion sets. Sufficient conditions for the long and short range dependence of α-stable moving averages are proven in terms of integrability of the corresponding kernel functions. For max-stable processes, the extremal coefficient function is used to state a necessary and sufficient condition for long range dependence.
Keywords: 519; long/short memory; long/short range dependence; alpha-stable; max-stable; level set; characteristic function; moving average; Brown-Resnick process; extremal Gaussian process; positive association; extremal coefficient