3 results found
Rowinska P, Veraart A, Gruet P, 2018, A multifactor approach to modelling the impact of wind energy on electricity spot prices, Publisher: SSRN
We introduce a three-factor model of electricity spot prices, consisting of a determinis-tic seasonality and trend function as well as short- and long-term stochastic components,and derive a formula for futures prices. The long-term component is modelled as a L ́evyprocess with increments belonging to the class of generalised hyperbolic distributions. We de-scribe the short-term factor by L ́evy semistationary processes: we start from a CARMA(2,1),i.e. a continous-time ARMA model, and generalise it by adding a short-memory stochasticvolatility. We further modify the model by including the information about the wind energyproduction as an exogenous variable. We fit our models to German and Austrian data in-cluding spot and futures prices as well as the wind energy production and total load data.Empirical studies reveal that taking into account the impact of the wind energy generation onthe prices improves the goodness of fit.
Rowinska P, Bodnar M, XXI National Conference on Applications of Mathematics in Biology and Medicine, XXI National Conference on Applications of Mathematics in Biology and Medicine
Rowinska P, Everitt RG, Delayed acceptance ABC-SMC, Journal of Computational and Graphical Statistics, ISSN: 1061-8600
Approximate Bayesian computation (ABC) is now an established technique for statistical inference used in cases where the likelihood function is computationally expensive or not available. It relies on the use of a model that is specified in the form of a simulator, and approximates the likelihood at a parameter θ by simulating auxiliary data sets x and evaluating the distance of x from the true data y. However, ABC is not computationally feasible in cases where using the simulator for each θ is very expensive. This paper investigates this situation in cases where a cheap, but approximate, simulator is available. The approach is to employ delayed acceptance Markov chain Monte Carlo (MCMC) within an ABC sequential Monte Carlo (SMC) sampler in order to, in a first stage of the kernel, use the cheap simulator to rule out parts of the parameter space that are not worth exploring, so that the "true" simulator is only run (in the second stage of the kernel) where there is a reasonable chance of accepting proposed values of θ. We show that this approach can be used quite automatically, with the only tuning parameter choice additional to ABC-SMC being the number of particles we wish to carry through to the second stage of the kernel. Applications to stochastic differential equation models and latent doubly intractable distributions are presented.
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