The unusual properties of aggregated superpositions of Ornstein-Uhlenbeck type processes
Leonenko, Nikolai N.
Taqqu, Murad S.
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Citation (published version)Danijel Grahovac, Nikolai N Leonenko, Anna Sikorskii, Murad S Taqqu. 2018. "The unusual properties of aggregated superpositions of Ornstein-Uhlenbeck type processes." Bernoulli, Volume 25, Number 3 (2019), 2029-2050. https://doi.org/10.3150/18-BEJ1044
Superpositions of Ornstein-Uhlenbeck type (supOU) processes form a rich class of stationary processes with a flexible dependence structure. The asymptotic behavior of the integrated and partial sum supOU processes can be, however, unusual. Their cumulants and moments turn out to have an unexpected rate of growth. We identify the property of fast growth of moments or cumulants as intermittency.