Semi-parametric forecasting of spikes in electricity prices

The occurrence of extreme movements in the spot price of electricity represents a significant source of risk to retailers. A range of approaches have been considered with respect to modelling electricity prices; these models, however, have relied on time-series approaches, which typically use restrictive decay schemes placing greater weight on more recent observations. This study develops an alternative, semi-parametric method for forecasting, which uses state-dependent weights derived from a kernel function. The forecasts that are obtained using this method are accurate and therefore potentially useful to electricity retailers in terms of risk management.

Mixed models for short-run forecasting of electricity prices: Application for the Spanish market

Short-run forecasting of electricity prices has become necessary for power generation unit schedule, since it is the basis of every profit maximization strategy. In this article a new and very easy method to compute accurate forecasts for electricity prices using mixed models is proposed. The main idea is to develop an efficient tool for one-step-ahead forecasting in the future, combining several prediction methods for which forecasting performance has been checked and compared for a span of several years. Also as a novelty, the 24 hourly time series has been modelled separately, instead of the complete time series of the prices. This allows one to take advantage of the homogeneity of these 24 time series. The purpose of this paper is to select the model that leads to smaller prediction errors and to obtain the appropriate length of time to use for forecasting. These results have been obtained by means of a computational experiment. A mixed model which combines the advantages of the two new models discussed is proposed. Some numerical results for the Spanish market are shown, but this new methodology can be applied to other electricity markets as well

Modelling Spikes in Electricity Prices

uring periods of market stress, electricity prices can rise dramatically. Electricity retailers cannot pass these extreme prices on to customers because of retail price regulation. Improved prediction of these price spikes therefore is important for risk management. This paper builds a time-varying-probability Markov-switching model of Queensland electricity prices, aimed particularly at forecasting price spikes. Variables capturing demand and weather patterns are used to drive the transition probabilities. Unlike traditional Markov-switching models that assume normality of the prices in each state, the model presented here uses a generalised beta distribution to allow for the skewness in the distribution of electricity prices during high-price episodes.

Forecasting Electricity Prices and their volatilities using Unobserved Components.

The liberalization of electricity markets more than ten years ago in the vast majority of developed countries has introduced the need of modelling and forecasting electricity prices and volatilities, both in the short and long term. Thus, there is a need of providing methodology that is able to deal with the most important features of electricity price series, which are well known for presenting not only structure in conditional mean but also time-varying conditional variances. In this work we propose a new model, which allows to extract conditionally heteroskedastic common factors from the vector of electricity prices. These common factors are jointly estimated as well as their relationship with the original vector of series, and the dynamics affecting both their conditional mean and variance. The estimation of the model is carried out under the state-space formulation. The new model proposed is applied to extract seasonal common dynamic factors as well as common volatility factors for electricity prices and the estimation results are used to forecast electricity prices and their volatilities in the Spanish zone of the Iberian Market. Several simplified/alternative models are also considered as benchmarks to illustrate that the proposed approach is superior to all of them in terms of explanatory and predictive power.

Modelling and forecasting fossil fuels, CO2 and electricity prices and their volatilities

In the current uncertain context that affects both the world economy and the energy sector, with the rapid increase in the prices of oil and gas and the very unstable political situation that affects some of the largest raw materials’ producers, there is a need for developing efficient and powerful quantitative tools that allow to model and forecast fossil fuel prices, CO2 emission allowances prices as well as electricity prices. This will improve decision making for all the agents involved in energy issues. Although there are papers focused on modelling fossil fuel prices, CO2 prices and electricity prices, the literature is scarce on attempts to consider all of them together. This paper focuses on both building a multivariate model for the aforementioned prices and comparing its results with those of univariate ones, in terms of prediction accuracy (univariate and multivariate models are compared for a large span of days, all in the first 4 months in 2011) as well as extracting common features in the volatilities of the prices of all these relevant magnitudes. The common features in volatility are extracted by means of a conditionally heteroskedastic dynamic factor model which allows to solve the curse of dimensionality problem that commonly arises when estimating multivariate GARCH models. Additionally, the common volatility factors obtained are useful for improving the forecasting intervals and have a nice economical interpretation. Besides, the results obtained and methodology proposed can be useful as a starting point for risk management or portfolio optimization under uncertainty in the current context of energy markets.

Optimal Combined Forecasts for Electricity Prices: Influence of Clean Energies

In this work, an electricity price forecasting model is developed. The performance of the proposed approach is improved by considering renewable energies (wind power and hydro generation) as explanatory variables. Additionally, the resulting forecasts are obtained as an optimal combination of a set of several univariate and multivariate time series models. The large computational experiment carried out using out-of-sample forecasts for every hour and day allows withdrawing statistically sound conclusions

Az európai villamosenergia-árak központi szabályozásának hatása a fogyasztói árakra (The impacts of the price regulation on the level of retail electricity prices in Europe)

Az Európai Unión belül az elmúlt időszakban megerősödött a vita arról, vajon a Közösség versenyképességének javításához milyen módon és mértékben járulhat hozzá az ipari és lakossági fogyasztók számára kedvező áron elérhető villamos energia. Az uniós testületek elsődlegesen a verseny feltételeinek további javításában látják a versenyképesség javításának fő eszközét, ám egyesek az aktívabb központi szabályozás mellett érvelnek. A jelenleg alkalmazott európai szabályozási gyakorlat áttekintése, a szabályozási modellek és a piaci árak alakulásának vizsgálata hozzásegíthet, hogy következtetéseket vonjunk le a tagállami gyakorlatok tekintetében, vajon sikeresebb-e a központi ármegállapításon alapuló szabályozói mechanizmus, mint a liberalizált piacmodell. ______ There is a strengthening debate within the European Union in recent years about the impact of the affordable industrial and household electricity prices on the general competitiveness of European economies. While the European Institutions argues for the further liberalization of the energy retail sector, there are others who believe in centralization and price control to achieve lower energy prices. Current paper reviews the regulatory models of the European countries and examines the connection between the regulatory regime and consumer price trends. The analysis can help to answer, whether the bureaucratic central regulation or the liberalized market model seems more successful in supporting the competitiveness goals. Although the current regulatory practice is heterogeneous within the EU member states, there is a clear trend to decrease the role of regulated tariffs in the end-user prices. Our study did not find a general causal relationship between the regulatory regime and the level of consumer electricity prices in a country concerned. However, the quantitative analysis of the industrial and household energy prices by various segments detected significant differences between the regulated and free-market countries. The first group of member states tends to decrease the prices in the low-consuming household segments through cross-financing technics, including increased network tariffs and/or taxes for the high-consuming segments and for industrial consumers. One of the major challenges of the regulatory authorities is to find the proper way of sharing these burdens proportionally with minimizing the market-distorting effects of the cross-subsidization between the different stakeholder groups.

Mathematical models for describing the shape of the in vitro unstretched human crystalline lens

We developed orthogonal least-squares techniques for fitting crystalline lens shapes, and used the bootstrap method to determine uncertainties associated with the estimated vertex radii of curvature and asphericities of five different models. Three existing models were investigated including one that uses two separate conics for the anterior and posterior surfaces, and two whole lens models based on a modulated hyperbolic cosine function and on a generalized conic function. Two new models were proposed including one that uses two interdependent conics and a polynomial based whole lens model. The models were used to describe the in vitro shape for a data set of twenty human lenses with ages 7–82 years. The two-conic-surface model (7 mm zone diameter) and the interdependent surfaces model had significantly lower merit functions than the other three models for the data set, indicating that most likely they can describe human lens shape over a wide age range better than the other models (although with the two-conic-surfaces model being unable to describe the lens equatorial region). Considerable differences were found between some models regarding estimates of radii of curvature and surface asphericities. The hyperbolic cosine model and the new polynomial based whole lens model had the best precision in determining the radii of curvature and surface asphericities across the five considered models. Most models found significant increase in anterior, but not posterior, radius of curvature with age. Most models found a wide scatter of asphericities, but with the asphericities usually being positive and not significantly related to age. As the interdependent surfaces model had lower merit function than three whole lens models, there is further scope to develop an accurate model of the complete shape of human lenses of all ages. The results highlight the continued difficulty in selecting an appropriate model for the crystalline lens shape.

A systematic review of mathematical models of mosquito-borne pathogen transmission: 1970-2010

Mathematical models of mosquito-borne pathogen transmission originated in the early twentieth century to provide insights into how to most effectively combat malaria. The foundations of the Ross–Macdonald theory were established by 1970. Since then, there has been a growing interest in reducing the public health burden of mosquito-borne pathogens and an expanding use of models to guide their control. To assess how theory has changed to confront evolving public health challenges, we compiled a bibliography of 325 publications from 1970 through 2010 that included at least one mathematical model of mosquito-borne pathogen transmission and then used a 79-part questionnaire to classify each of 388 associated models according to its biological assumptions. As a composite measure to interpret the multidimensional results of our survey, we assigned a numerical value to each model that measured its similarity to 15 core assumptions of the Ross–Macdonald model. Although the analysis illustrated a growing acknowledgement of geographical, ecological and epidemiological complexities in modelling transmission, most models during the past 40 years closely resemble the Ross–Macdonald model. Modern theory would benefit from an expansion around the concepts of heterogeneous mosquito biting, poorly mixed mosquito-host encounters, spatial heterogeneity and temporal variation in the transmission process.

Mathematical models of bubble evolution in a Hele-Shaw Cell

This thesis concerns the mathematical model of moving fluid interfaces in a Hele-Shaw cell: an experimental device in which fluid flow is studied by sandwiching the fluid between two closely separated plates. Analytic and numerical methods are developed to gain new insights into interfacial stability and bubble evolution, and the influence of different boundary effects is examined. In particular, the properties of the velocity-dependent kinetic undercooling boundary condition are analysed, with regard to the selection of only discrete possible shapes of travelling fingers of fluid, the formation of corners on the interface, and the interaction of kinetic undercooling with the better known effect of surface tension. Explicit solutions to the problem of an expanding or contracting ring of fluid are also developed.