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Multivariate CARMA processes

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  • Marquardt, Tina
  • Stelzer, Robert

Abstract

A multivariate Lévy-driven continuous time autoregressive moving average (CARMA) model of order (p,q), q

Suggested Citation

  • Marquardt, Tina & Stelzer, Robert, 2007. "Multivariate CARMA processes," Stochastic Processes and their Applications, Elsevier, vol. 117(1), pages 96-120, January.
    • Handle: RePEc:eee:spapps:v:117:y:2007:i:1:p:96-120
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    References listed on IDEAS

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    1. P. Brockwell, 2001. "Lévy-Driven Carma Processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(1), pages 113-124, March.
    2. Sato, Ken-iti & Yamazato, Makoto, 1984. "Operator-selfdecomposable distributions as limit distributions of processes of Ornstein-Uhlenbeck type," Stochastic Processes and their Applications, Elsevier, vol. 17(1), pages 73-100, May.
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    Citations

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    Cited by:

    1. Vicky Fasen-Hartmann & Celeste Mayer, 2022. "Whittle estimation for continuous-time stationary state space models with finite second moments," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(2), pages 233-270, April.
    2. Appleby, John A.D. & Patterson, Denis D., 2021. "Growth and fluctuation in perturbed nonlinear Volterra equations," Applied Mathematics and Computation, Elsevier, vol. 396(C).
    3. Vicky Fasen‐Hartmann & Sebastian Kimmig, 2020. "Robust estimation of stationary continuous‐time arma models via indirect inference," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(5), pages 620-651, September.
    4. Vicky Fasen, 2016. "Dependence Estimation for High-frequency Sampled Multivariate CARMA Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(1), pages 292-320, March.
    5. Florian Fuchs & Robert Stelzer, 2013. "Spectral Representation of Multivariate Regularly Varying Lévy and CARMA Processes," Journal of Theoretical Probability, Springer, vol. 26(2), pages 410-436, June.
    6. P. Brockwell, 2014. "Recent results in the theory and applications of CARMA processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(4), pages 647-685, August.
    7. Nielsen, Mikkel Slot, 2020. "On non-stationary solutions to MSDDEs: Representations and the cointegration space," Stochastic Processes and their Applications, Elsevier, vol. 130(5), pages 3154-3173.
    8. Fasen, Vicky & Fuchs, Florian, 2013. "On the limit behavior of the periodogram of high-frequency sampled stable CARMA processes," Stochastic Processes and their Applications, Elsevier, vol. 123(1), pages 229-273.
    9. Holger Fink, 2016. "Conditional Distributions of Mandelbrot–van ness Fractional LÉVY Processes and Continuous-Time ARMA–GARCH-Type Models with Long Memory," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(1), pages 30-45, January.
    10. Brockwell, Peter J. & Schlemm, Eckhard, 2013. "Parametric estimation of the driving Lévy process of multivariate CARMA processes from discrete observations," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 217-251.
    11. Mercuri, Lorenzo & Perchiazzo, Andrea & Rroji, Edit, 2024. "A Hawkes model with CARMA(p,q) intensity," Insurance: Mathematics and Economics, Elsevier, vol. 116(C), pages 1-26.
    12. Basse-O’Connor, Andreas & Nielsen, Mikkel Slot & Pedersen, Jan & Rohde, Victor, 2019. "Multivariate stochastic delay differential equations and CAR representations of CARMA processes," Stochastic Processes and their Applications, Elsevier, vol. 129(10), pages 4119-4143.
    13. Benth, Fred Espen & Karbach, Sven, 2023. "Multivariate continuous-time autoregressive moving-average processes on cones," Stochastic Processes and their Applications, Elsevier, vol. 162(C), pages 299-337.
    14. Fasen-Hartmann, Vicky & Mayer, Celeste, 2023. "Empirical spectral processes for stationary state space models," Stochastic Processes and their Applications, Elsevier, vol. 155(C), pages 319-354.
    15. Péter Kevei, 2018. "Asymptotic moving average representation of high-frequency sampled multivariate CARMA processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(2), pages 467-487, April.
    16. Valentin Courgeau & Almut E. D. Veraart, 2020. "High-frequency Estimation of the L\'evy-driven Graph Ornstein-Uhlenbeck process," Papers 2008.10930, arXiv.org, revised Jul 2022.

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