Multivariate supOU processes

By Ole E. Barndorff-Nielsen, Robert Stelzer. 2010

92 citations recorded by the source corpus.

Univariate superpositions of Ornstein–Uhlenbeck-type processes (OU), called supOU processes, provide a class of continuous time processes capable of exhibiting long memory behavior. This paper introduces multivariate supOU processes and gives conditions for their existence and finiteness of moments. Moreover, the second-order moment structure is explicitly calculated, and examples exhibit the possibility of long-range dependence. Our supOU processes are defined via homogeneous and factorizable Levy bases. We show that the behavior of supOU processes is particularly nice when the mean reversion parameter is restricted to normal matrices and especially to strictly negative definite ones. For finite variation Levy bases we are able to give conditions for supOU processes to have locally bounded cadlag paths of finite variation and to show an analogue of the stochastic differential equation of OU-type processes, which has been suggested in [2] in the univariate case. Finally, as an important special case, we introduce positive semi-definite supOU processes, and we discuss the relevance of multivariate supOU processes in applications.

Subfields: Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/73d1004beb412169e2b354e059579cd455218d4f

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Citations in the corpus

THE MULTIVARIATE supOU STOCHASTIC VOLATILITY MODEL (2013, methodology): “For proofs of the results in this section we refer to Barndorff-Nielsen and Stelzer (2009) .”
Modelling energy spot prices by volatility modulated Levy-driven Volterra processes (2013, result): “It should be noted that this type of “superposition” is quite different from the concept behind supOU processes as studied in, for example, Barndorff-Nielsen and Stelzer [15].”
Stochastic Volatility of Volatility and Variance Risk Premia (2013, unknown): “This is done by extensions of the idea of supOU processes, as introduced by Barndorff-Nielsen (2001) and further discussed in Barndorff-Nielsen & Shephard (2003), Barndorff-Nielsen & Leonenko (2005), Fasen & Klüppelberg (2007), Barndorff-Nielsen & Stelzer (2011),Barndorff-Nielsen & Stelzer (2012).”