Levy-driven CARMA models with applications to electricity markets, stochastic volatility and wind field models
This two-day intensive course will give an introduction to continuous-time autoregressive moving average (CARMA) processes with Levy noise. Such linear models can either be applied directly to electricity market data, where they fit remarkably well, or they can be used as linear approximations to non-linear phenomena like wind speed. Furthermore, they have also been used for stochastic volatility modeling, and they can serve as driving processes to advanced modeling of stochastic dynamics.
We will present and discuss the definition of CARMA processes, conditions for stationarity, and further probabilistic properties. We will also present statistical methods for parameter estimation. And finally, we will present relevant applications.
References
[1] Benth, F.E., Kluppelberg, C., Muller, G. and Vos, L. (2011) Futures pricing in electricity markets based on stable CARMA spot models. Submitted for publication.
[2] Brockwell, P. and Lindner, A. (2009) Existence and uniqueness of stationary Levy-driven CARMA processes. Stoch. Proc. Appl. 119(8), 2660-2681.
[3] Brockwell, P., Ferrazzano, E. and Kluppelberg, C. (2011) High-frequency sampling and kernel estimation for continuous-time moving average processes. Submitted for publication.
[4] Todorov, V. and Tauchen, G. (2006) Simulation methods for Levy-driven CARMA stochastic volatility models. Journal of Business and Economic Statistics, 24(4), 450-469.
The two-day intensive course will be given by Professor Claudia Kluppelberg (Technical University Munchen). The intended audience include researchers at PhD level or higher and analysts in industry in the fields of energy market modelling and stochastics. Quantitatively-oriented master students are also welcome to attend. The course will take place Wednesday and Thursday, September 12-13, 2012. The lectures will start each day at 9.15, and end at 15.00. There is a lunch break from 12.30 until 13.30.
There is no participation fee. Please register your attendance by emailing the project leader of MAWREM, Professor Fred Espen Benth (fredb 'at' math.uio.no)
Slides from the first day can be found here: http://folk.uio.no/fredb/kluppelberg_slides.pdf
Papers describing the material in detail presented on day two can be downloaded from the web-page http://www-m4.ma.tum.de/forschung/preprints-veroeffentlichungen/