Statistical Modelling 11 (2011), 447–470

Estimation of stable CARMA models with an application to electricity spot prices

Isabel García
Department of Mathematics
Ruhr-Universität Bochum
Germany

Claudia Klüppelberg
Center for Mathematical Sciences and Institute for Advanced Study
Technische Universität München
Germany

Gernot Müller
Center for Mathematical Sciences
Technische Universität München
D–85747 Garching
Germany
eMail: mueller@ma.tum.de

Abstract:

We discuss theoretical properties and estimation of continuous-time ARMA (CARMA) processes, which are driven by a stable Lévy process. Such processes are very useful in a continuous-time linear stationary setup: they have a similar structure as the widely used ARMA models and provide all advantages of a continuous-time model. As an application we consider data from a deregulated electricity market. Here, we fit a CARMA(2,1) model to spot prices from the Singapore New Electricity Market. The quality of the estimates is assessed in a simulation study. The continuous-time modelling aims at a new pricing methodology for energy derivatives.

Keywords:

CARMA model; electricity prices; estimation of CARMA models; stable CARMA model; stable Lévy process; stable Ornstein-Uhlenbeck process

Downloads:

The data used in the paper can be downloaded for free at www.ema.gov.sg . The software STABLE used in Section 5.2 is available from J.P.Nolan's website academic2.american.edu/~jpnolan.

Matlab code to calculate CARMA(2,1) parameters from estimated ARMA(2,1) parameters are in zipped archive.


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