Superpositions of CARMA processes

Danijel Grahovac; Magdalena Mikić

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arXiv · 2601.15796

Superpositions of CARMA processes

Danijel Grahovac·Magdalena Mikić

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Abstract

We introduce supCARMA processes, defined as superpositions of L\'evy-driven CARMA processes with respect to a L\'evy basis, as a natural extension of the superpositions of Ornstein-Uhlenbeck type processes. We then focus on supCAR$(2)$ processes and show that they can be classified into three distinct types determined by the eigenstructure of the underlying CAR$(2)$ matrix. For each type we provide conditions for existence and derive explicit expressions for the correlation function. The resulting correlation structures may exhibit long-range dependence and can be non-monotone. These features make supCAR$(2)$ processes a flexible class for modeling time series with oscillatory correlations or strong dependence.

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Danijel Grahovac, Magdalena Mikić. 2026-01-22. Superpositions of CARMA processes. https://arxiv.org/abs/2601.15796

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