Stochastic Analysis and Applications· 2026Q2
Superpositions of CARMA processes
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- Q2SCImago
- 2026year
Short summary
Researchers introduce supCARMA processes, superpositions of Lévy-driven CARMA processes, as a flexible new class for modeling time series with complex correlation structures, including long-range dependence and non-monotone patterns.
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Key points
- Introduced supCARMA processes as superpositions of Lévy-driven CARMA processes.
- Classified supCAR(2) processes into three types based on CAR(2) matrix eigenstructure.
- Derived explicit conditions for existence and correlation functions for supCAR(2) processes.
- Identified potential for long-range dependence and non-monotone correlation structures.
AI-generated from the title and abstract; the full text is not read.
Abstract
We introduce supCARMA processes, defined as superpositions of Lévy-driven CARMA processes with respect to a Lévy 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.
The authors' abstract, as published at the source. Stochastic Analysis and Applications, 2026 · DOI ↗
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Field: Finance
FinanceEconomics, Econometrics and Finance