Some New Approaches to Forecasting the Price of Electricity: A Study of Californian Market

In this paper we consider the forecasting performance of a range of semi- and non- parametric methods applied to high frequency electricity price data. Electricity price time-series data tend to be highly seasonal, mean reverting with price jumps/spikes and time- and price-dependent volatility. The typical approach in this area has been to use a range of tools that have proven popular in the financial econometrics literature, where volatility clustering is common. However, electricity time series tend to exhibit higher volatility on a daily basis, but within a mean reverting framework, albeit with occasional large ’spikes’. In this paper we compare the existing forecasting performance of some popular parametric methods, notably GARCH AR-MAX, with approaches that are new to this area of applied econometrics, in particular, Artificial Neural Networks (ANN); Linear Regression Trees, Local Regressions and Generalised Additive Models. Section 2 presents the properties and definitions of the models to be compared and Section 3 the characteristics of the data used which in this case are spot electricity prices from the Californian market 07/1999-12/2000. This period includes the ’crisis’ months of May-August 2000 where extreme volatility was observed. Section 4 presents the results and ranking of methods on the basis of forecasting performance. Section 5 concludes.Electricty Time Series; Forecasting Performance; Semi- and Non- Parametric Methods

An extended space approach for particle Markov chain Monte Carlo methods

In this paper we consider fully Bayesian inference in general state space models. Existing particle Markov chain Monte Carlo (MCMC) algorithms use an augmented model that takes into account all the variable sampled in a sequential Monte Carlo algorithm. This paper describes an approach that also uses sequential Monte Carlo to construct an approximation to the state space, but generates extra states using MCMC runs at each time point. We construct an augmented model for our extended space with the marginal distribution of the sampled states matching the posterior distribution of the state vector. We show how our method may be combined with particle independent Metropolis-Hastings or particle Gibbs steps to obtain a smoothing algorithm. All the Metropolis acceptance probabilities are identical to those obtained in existing approaches, so there is no extra cost in term of Metropolis-Hastings rejections when using our approach. The number of MCMC iterates at each time point is chosen by the used and our augmented model collapses back to the model in Olsson and Ryden (2011) when the number of MCMC iterations reduces. We show empirically that our approach works well on applied examples and can outperform existing methods.Comment: 35 pages, 2 figures, Typos corrected from Version

Structure Selection of Polynomial NARX Models using Two Dimensional (2D) Particle Swarms

The present study applies a novel two-dimensional learning framework (2D-UPSO) based on particle swarms for structure selection of polynomial nonlinear auto-regressive with exogenous inputs (NARX) models. This learning approach explicitly incorporates the information about the cardinality (i.e., the number of terms) into the structure selection process. Initially, the effectiveness of the proposed approach was compared against the classical genetic algorithm (GA) based approach and it was demonstrated that the 2D-UPSO is superior. Further, since the performance of any meta-heuristic search algorithm is critically dependent on the choice of the fitness function, the efficacy of the proposed approach was investigated using two distinct information theoretic criteria such as Akaike and Bayesian information criterion. The robustness of this approach against various levels of measurement noise is also studied. Simulation results on various nonlinear systems demonstrate that the proposed algorithm could accurately determine the structure of the polynomial NARX model even under the influence of measurement noise

ESTIMATION AND ASYMPTOTIC THEORY FOR A NEW CLASS OF MIXTURE MODELS

In this paper a new model of mixture of distributions is proposed, where the mixing structure is determined by a smooth transition tree architecture. Models based on mixture of distributions are useful in order to approximate unknown conditional distributions of multivariate data. The tree structure yields a model that is simpler, and in some cases more interpretable, than previous proposals in the literature. Based on the Expectation-Maximization (EM) algorithm a quasi-maximum likelihood estimator is derived and its asymptotic properties are derived under mild regularity conditions. In addition, a specific-to-general model building strategy is proposed in order to avoid possible identification problems. Both the estimation procedure and the model building strategy are evaluated in a Monte Carlo experiment, which give strong support for the theory developed in small samples. The approximation capabilities of the model is also analyzed in a simulation experiment. Finally, two applications with real datasets are considered. KEYWORDS: Mixture models, smooth transition, EM algorithm, asymptotic properties, time series, conditional distribution.

Nonlinear Cointegration, Misspecification and Bimodality

We show that the asymptotic distribution of the ordinary least squares estimator in a cointegration regression may be bimodal. A simple case arises when the intercept is erroneously omitted from the estimated model or in nonlinear-in-variables models with endogenous regressors. In the latter case, a solution is to use an instrumental variable estimator. The core results in this paper also generalises to more complicated nonlinear models involving integrated time series.Cointegration, nonlinearity, bimodality, misspecification, instrumental variables, asymptotic theory.

Long memory or shifting means? A new approach and application to realised volatility

It is now recognised that long memory and structural change can be confused because the statistical properties of times series of lengths typical of financial and econometric series are similar for both models. We propose a new set of methods aimed at distinguishing between long memory and structural change. The approach, which utilises the computational efficient methods based upon Atheoretical Regression Trees (ART), establishes through simulation the bivariate distribution of the fractional integration parameter, d, with regime length for simulated fractionally integrated series. This bivariate distribution is then compared with the data for the time series. We also combine ART with the established goodness of fit test for long memory series due to Beran. We apply these methods to the realized volatility series of 16 stocks in the Dow Jones Industrial Average. We show that in these series the value of the fractional integration parameter is not constant with time. The mathematical consequence of this is that the definition of H self-similarity is violated. We present evidence that these series have structural breaks.Long-range dependence; Strong dependence; Global dependence; Hurst phenomena

SocialDTN: A DTN implementation for Digital and Social Inclusion

Despite of the importance of access to computers and to the Internet for the development of people and their inclusion in society, there are people that still suffer with digital divide and social exclusion. Delay/Disruption-Tolerant Networking (DTN) can help the digital/social inclusion of these people as it allows opportunistic and asynchronous communication, which does not depend upon networking infrastructure. We introduce SocialDTN, an implementation of the DTN architecture for Android devices that operates over Bluetooth, taking advantages of the social daily routines of users. As we want to exploit the social proximity and interactions existing among users, SocialDTN includes a social-aware opportunistic routing proposal, dLife, instead of the well-known (but social-oblivious) PROPHET. Simulations show the potential of dLife for our needs. Additionally, some preliminary results from field experimentations are presented.Comment: 3 pages, 4 figure