Modeling and forecasting electricity spot prices: A functional data perspective

Classical time series models have serious difficulties in modeling and forecasting the enormous fluctuations of electricity spot prices. Markov regime switch models belong to the most often used models in the electricity literature. These models try to capture the fluctuations of electricity spot prices by using different regimes, each with its own mean and covariance structure. Usually one regime is dedicated to moderate prices and another is dedicated to high prices. However, these models show poor performance and there is no theoretical justification for this kind of classification. The merit order model, the most important micro-economic pricing model for electricity spot prices, however, suggests a continuum of mean levels with a functional dependence on electricity demand. We propose a new statistical perspective on modeling and forecasting electricity spot prices that accounts for the merit order model. In a first step, the functional relation between electricity spot prices and electricity demand is modeled by daily price-demand functions. In a second step, we parameterize the series of daily price-demand functions using a functional factor model. The power of this new perspective is demonstrated by a forecast study that compares our functional factor model with two established classical time series models as well as two alternative functional data models.Comment: Published in at http://dx.doi.org/10.1214/13-AOAS652 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Estimation of the Semiparametric Factor Model: Application to Modelling Time Series of Electricity Spot Prices.

Classical univariate and multivariate time series models have problems to deal with the high variability of hourly electricity spot prices. We propose to model alternatively the daily mean electricity supply functions using a dynamic factor model. And to derive, subsequently, the hourly electricity spot prices by the evaluation of the estimated supply functions at the corresponding hourly values of demand for electricity. Supply functions are price (EUR/MWh) functions, that increase monotonically with demand for electricity (MW). Apart from this new conceptual approach, that allows us to represent the auction design of energy exchanges in a most natural way, our main contribution is an extraordinary simple algorithm to estimate the factor structure of the dynamic factor model. We decompose the time series into a functional spherical component and an univariate scaling component. The elements of the spherical component are all standardized having unit size such that we can robustly estimate the factor structure. This algorithm is much simpler than procedures suggested in the literature. In order to use a parsimonious labeling we will refer to the daily mean supply curves simply as price curves.Factor Analysis; functional time series data; sparse data; electricity spot market prices; European Electricity Exchange (EEX)

The R-package phtt: Panel Data Analysis with Heterogeneous Time Trends

The R-package phtt provides estimation procedures for panel data with large dimensions n, T, and general forms of unobservable heterogeneous effects. Particularly, the estimation procedures are those of Bai (2009) and Kneip, Sickles, and Song (2012), which complement one another very well: both models assume the unobservable heterogeneous effects to have a factor structure. Kneip et al. (2012) considers the case in which the time varying common factors have relatively smooth patterns including strongly positive auto-correlated stationary as well as non-stationary factors, whereas the method of Bai (2009) focuses on stochastic bounded factors such as ARMA processes. Additionally, the phtt package provides a wide range of dimensionality criteria in order to estimate the number of the unobserved factors simultaneously with the remaining model parameters

Skin Cell Proliferation Stimulated by Microneedles

A classical wound may be defined as a disruption of tissue integrity. Wounds, caused by trauma from accidents or surgery, that close via secondary intention rely on the biological phases of healing, i.e., hemostasis, inflammation, proliferation, and remodeling (HIPR). Depending on the wound type and severity, the inflammation phase begins immediately after injury and may last for an average of 7–14 days. Concurrent with the inflammation phase or slightly delayed, cell proliferation is stimulated followed by the activation of the remodeling (maturation) phase. The latter phase can last as long as 1 year or more, and the final healed state is represented by a scar tissue, a cross-linked collagen formation that usually aligns collagen fibers in a single direction. One may assume that skin microneedling that involves the use of dozens or as many as 200 needles that limit penetration to 1.5 mm over 1 cm2 of skin would cause trauma and bleeding followed by the classical HIPR. However, this is not the case or at least the HIPR phases are significantly curtailed and healing never ends in a scar formation. Conversely dermabrasion used in aesthetic medicine for improving skin quality is based on “ablation” (destruction or wounding of superficial skin layers), which requires several weeks for healing that involves formation of new skin layers. Such procedures provoke an acute inflammatory response. We believe that a less intense inflammatory response occurs following microneedle perforation of the skin. However, the mechanism of action of microneedling appears to be different. Here we review the potential mechanisms by which microneedling of the skin facilitates skin repair without scarring after the treatment of superficial burns, acne, hyperpigmentation, and the non-advancing periwound skin surrounding the chronic ulcerations of the integument

Improving Estimation in Functional Linear Regression with Points of Impact: Insights into Google AdWords

The functional linear regression model with points of impact is a recent augmentation of the classical functional linear model with many practically important applications. In this work, however, we demonstrate that the existing data-driven procedure for estimating the parameters of this regression model can be very instable and inaccurate. The tendency to omit relevant points of impact is a particularly problematic aspect resulting in omitted-variable biases. We explain the theoretical reason for this problem and propose a new sequential estimation algorithm that leads to significantly improved estimation results. Our estimation algorithm is compared with the existing estimation procedure using an in-depth simulation study. The applicability is demonstrated using data from Google AdWords, today's most important platform for online advertisements. The \textsf{R}-package \texttt{FunRegPoI} and additional \textsf{R}-codes are provided in the online supplementary material