Electricity Price Time Series Research Articles

A mixed integer linear program to compress transition probability matrices in Markov chain bootstrapping

Bootstrapping time series is one of the most acknowledged tools to study the statistical properties of an evolutive phenomenon. An important class of bootstrapping methods is based on the assumption that the sampled phenomenon evolves according to a Markov chain. This assumption does not apply when the process takes values in a continuous set, as it frequently happens with time series related to economic and financial phenomena. In this paper we apply the Markov chain theory for bootstrapping continuous-valued processes, starting from a suitable discretization of the support that provides the state space of a Markov chain of order \(k \ge 1\). Even for small k, the number of rows of the transition probability matrix is generally too large and, in many practical cases, it may incorporate much more information than it is really required to replicate the phenomenon satisfactorily. The paper aims to study the problem of compressing the transition probability matrix while preserving the “law” characterising the process that generates the observed time series, in order to obtain bootstrapped series that maintain the typical features of the observed time series. For this purpose, we formulate a partitioning problem of the set of rows of such a matrix and propose a mixed integer linear program specifically tailored for this particular problem. We also provide an empirical analysis by applying our model to the time series of Spanish and German electricity prices, and we show that, in these medium size real-life instances, bootstrapped time series reproduce the typical features of the ones under observation.

Short-Term Wind Speed Forecasting Study and Its Application Using a Hybrid Model Optimized by Cuckoo Search

The support vector regression (SVR) and neural network (NN) are both new tools from the artificial intelligence field, which have been successfully exploited to solve various problems especially for time series forecasting. However, traditional SVR and NN cannot accurately describe intricate time series with the characteristics of high volatility, nonstationarity, and nonlinearity, such as wind speed and electricity price time series. This study proposes an ensemble approach on the basis of 5-3 Hanning filter (5-3H) and wavelet denoising (WD) techniques, in conjunction with artificial intelligence optimization based SVR and NN model. So as to confirm the validity of the proposed model, two applicative case studies are conducted in terms of wind speed series from Gansu Province in China and electricity price from New South Wales in Australia. The computational results reveal that cuckoo search (CS) outperforms both PSO and GA with respect to convergence and global searching capacity, and the proposed CS-based hybrid model is effective and feasible in generating more reliable and skillful forecasts.

Can negative electricity prices encourage inefficient electrical energy storage devices?

This paper explores whether negative electricity prices can change the rationale that efficient energy storage devices are more economical for arbitrage in electricity markets. An established model algorithm to determine the maximum available arbitrage revenue and optimum schedule of electrical energy storage (EES) operation is used to simulate storage with a time-series of electricity prices which includes some negative prices. Our results suggest that at any likely frequency of negative electricity prices, inefficient EES is not encouraged, and can only be encouraged for EES devices with very low energy capacity to power ratios.

Efficient modeling and forecasting of electricity spot prices

The increasing importance of renewable energy, especially solar and wind power, has led to new forces in the formation of electricity prices. Hence, this paper introduces an econometric model for the hourly time series of electricity prices of the European Power Exchange (EPEX) which incorporates specific features like renewable energy. The model consists of several sophisticated and established approaches and can be regarded as a periodic VAR-TARCH with wind power, solar power, and load as influences on the time series. It is able to map the distinct and well-known features of electricity prices in Germany. An efficient iteratively reweighted lasso approach is used for the estimation. Moreover, it is shown that several existing models are outperformed by the procedure developed in this paper.

Component estimation for electricity prices: Procedures and comparisons

Electricity price time series usually exhibit some form of nonstationarity, corresponding to long-term behavior, one or more periodic components as well as dependence on calendar effects. As a result, modeling electricity prices requires accounting for both long-term and periodic components. In the literature, several filtering procedures have been proposed but a standard has not yet been found. Furthermore, since different procedures are applied in contexts that are not homogeneous with respect to data, periods and final goals, a fair comparison is difficult. This work considers several methods for component estimation in a homogeneous framework and compares them according to specific criteria. The final purpose is to find an estimation procedure that performs well, independently of the intended market and that can be proposed as a reference for electricity price time series filtering.

A hybrid intelligent model based on recurrent neural networks and excitable dynamics for price prediction in deregulated electricity market

This paper examines electricity price time series from dynamical system perspective and proposes a hybrid model which employs a synergistic combination of Recurrent Neural Network (RNN) and coupled excitable system for prediction of future prices in deregulated electricity markets. Driven by profit maximizing decisions taken by various agents, these markets belong to the class of financial systems. However presence of intermittent spikes and complex dynamic nonlinearities in electricity price time series render the prediction task extremely challenging. The approximation ability of Recurrent Neural Networks to map dynamic functions together with sharp jumping attribute of coupled excitable systems allows close approximation of spiky time series. The developed hybrid model was applied for point and interval forecasting in various markets worldwide over different seasons for testing its adaptability in different environments. Satisfactory prediction results were obtained in all the markets, in stable as well as spiking regions of the time series.

A hybrid electricity price forecasting model for the Nordic electricity spot market

A hybrid electricity price forecasting model for the Finnish electricity spot market is proposed in this paper. The daily electricity price time series is analyzed in two layers – normal behavior and spiky behavior. Two different data preprocessing techniques are applied to handle trend and seasonality in the time series. ARMA-based model is used to catch the linear relationship between the normal range price series and the explanatory variable, GARCH model is used to unveil the heteroscedastic character of residuals, and a neural network is applied to combine predictions from ARMA-based and GARCH models with historical price and demand data to produce a final normal range price forecast. The probability of a price spike occurrence and the value of a price spike are produced by a Gaussian Mixture model and K-nearest neighboring model respectively. Forecasts of normal range prices and price spikes are generated to form an overall price forecast up to one week-ahead. The results show that hybridization of the normal range price and price spikes forecasts may provide extensive and valuable information for electricity market participants.

The contribution of heat storage to the profitable operation of combined heat and power plants in liberalized electricity markets

Combined heat and power (CHP) plants are characterized by high fuel efficiency and are therefore usually the thermal power producing units of choice within a district heating network. The operation of CHP units is typically controlled by the current heat demand and thus delimits the range of electricity production. Heat storage devices are a promising alternative to uncouple the heat load of the district heating network from the commitment of the units and to allow for price-oriented electricity production.In this paper we present numerical results for the combined optimization of the operation of nineteen existing power plant units and the design of six proposed heat accumulators which supply the district heating network of Berlin. A mixed-integer programming problem (MIP) is formulated in GAMS and solved with CPLEX. This paper focuses on the potential for increasing profitability through the addition of heat accumulators in the energy system described above, on the optimal storage capacities for different price scenarios (variation of fuel costs, prices for carbon dioxide emission certificates, and electricity price time series) as well as on the adjustment of the operation of the power plants due to heat storage.

ELECTRICITY PRICES: A NONPARAMETRIC APPROACH

We propose a simple univariate model for the dynamics of spot electricity prices. The model is nonparametric in the sense that it is free from parametric model assumptions and flexible in capturing the dynamics of the data. The estimation is performed in two steps. Preliminarily, spikes are identified by means of an iterative filtering technique. The series of spikes is used to estimate a seasonal spike intensity function and fitted with an exponential law. We then implement Nadaraya-Watson estimators for the drift and the diffusion coefficients on the filtered series. Monte Carlo simulations are used to evaluate estimation errors. We fit the model on European and American time series of spot day-ahead electricity prices; in spite of the simplicity of the proposed model, our specification tests indicate successful goodness-of-fit. We provide evidence for mean-reversion, nonlinear volatility and seasonal spike intensity; moreover we find that American markets show a very low level of mean reversion and a lower volatility with respect to their European counterparts.

Self exciting threshold auto-regressive approach for non-linear modeling of daily electricity prices in the selected regions

This paper is focused on the electricity market and electricity prices. The electricity sector is one of the key strategic sectors of every economy and knowledge of demand, supply and prices is very important. Because of the features occurring in the time series of electricity prices (i.e. high frequency, non-constant mean, autocorrelation, non-normal distribution, heteroscedasticity, seasonality, etc.), it is necessary to employ more sophisticated models for the purposes of their modeling. The goal of this paper is to propose the empirical model for modeling daily electricity prices in three selected regions (California, North Europe and Austria). To exploit non-linearity, we apply the SETAR (Self Exciting Threshold Auto-Regressive) models that imply and distinct regimes in time series dynamics with potentially different parameters (and thus dynamics properties) of each regime. First, the most appropriate SETAR model for modeling electricity prices at selected markets is developed; next, statistical verification of each model is performed in accordance with Hansen (1997, 2000); finally, it is verified whether the proposed non-linear models give satisfactory results in the sense of data fitting and diagnostic checks.

Electricity Prices: A Nonparametric Approach

We propose a simple univariate model for the dynamics of spot electricity prices. The model is nonparametric in the sense that it is free from parametric model assumptions and flexible in capturing the dynamics of the data. The estimation is performed in two steps. Preliminarily, spikes are identified by means of an iterative filtering technique. The series of spikes is used to estimate a seasonal jump intensity function. We then implement Nadaraya-Watson estimators for the drift and the diffusion coefficients on the filtered series. Monte Carlo simulations are used to evaluate estimation errors. We fit the model on European and American time series of spot day-ahead electricity prices; in spite of the simplicity of the proposed model, our specification tests indicate successful goodness-of-fit. We provide evidence for mean-reversion, nonlinear volatility and seasonal spike intensity; moreover we find that American markets show a very low level of mean reversion and a lower volatility with respect to their European counterparts.

Correlation of Electricity Prices in European Wholesale Power Markets

The time series of daily mean electricity prices which have been formed in European Power Exchanges are analyzed in this article. The objective of this work is to characterize the degree of correlation between prices in wholesale power markets, which are defined as environment where electricity generators and distributors deal. In a competitive environment these prices can be determined by supply and demand functions and are influenced by various factors such as fuel prices, temperature, wind speed, precipitations, CO2 and economic growth. As electricity prices have specific and unique characteristics, such as seasonality and highly volatile wholesale prices, they are motivated to use an appropriate time series model to study the relationship between prices in different European marketplaces. Considering this, additive regression model was used in order to estimate the relationship between prices in European wholesale markets. Correlation and regression analysis proved that bulk prices of electricity in Europe are heavily related but there are first initial steps of such correlation, although market design is similar among countries and there is an increase in spot market volume, where liquidity and foreign trade take place. Price analysis showed that wholesale prices in Finland, Sweden and Norway are lower than in other European power markets. It is not surprising, because the large proportion of energy is generated in hydro plants. On the other hand wholesale prices are very volatile in Germany, France and as it was seen prices started to rise since the beginning of 2005.

Modeling and Forecasting Electricity Prices with Input/Output Hidden Markov Models

In competitive electricity markets, in addition to the uncertainty of exogenous variables such as energy demand, water inflows, and availability of generation units and fuel costs, participants are faced with the uncertainty of their competitors' behavior. The analysis of electricity price time series reflects a switching nature, related to discrete changes in competitors' strategies, which can be represented by a set of dynamic models sequenced together by a Markov chain. An input-output hidden Markov model (IOHMM) is proposed for analyzing and forecasting electricity spot prices. The model provides both good predictions in terms of accuracy as well as dynamic information about the market. In this way, different market states are identified and characterized by their more relevant explanatory variables. Moreover, a conditional probability transition matrix governs the probabilities of remaining in the same state, or changing to another, whenever a new market session is opened. The model has been successfully applied to real clearing prices in the Spanish electricity market.