CARMA Processes driven by Non-Gaussian Noise

Details CARMA Processes driven by Non-Gaussian Noise CARMA Processes driven by Non-Gaussian Noise

2011-12-30

arxiv.org/abs/1201.0155v1

Robert Stelzer (2011), CARMA Processes driven by Non-Gaussian Noise,TUM-IAS Pimary Sources - Essays in Technology and Science,

Mathematics

Probability

Preprint version of article available at http://www.tum-ias.de/institute-for-advanced-study/publications/journal-primary-sourc

Scientific paper

We present an outline of the theory of certain L\'evy-driven, multivariate stochastic processes, where the processes are represented by rational transfer functions (Continuous-time AutoRegressive Moving Average or CARMA models) and their applications in non-Gaussian time series modelling. We discuss in detail their definition, their spectral representation, the equivalence to linear state space models and further properties like the second order structure and the tail behaviour under a heavy-tailed input. Furthermore, we study the estimation of the parameters using quasi-maximum likelihood estimates for the auto-regressive and moving average parameters, as well as how to estimate the driving L\'evy process.

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