Ellipsoidal Prediction Regions for Multivariate Uncertainty Characterization

While substantial advances are observed in probabilistic forecasting for power system operation and electricity market applications, most approaches are still developed in a univariate framework. This prevents from informing about the interdependence structure among locations, lead times and variables of interest. Such dependencies are key in a large share of operational problems involving renewable power generation, load and electricity prices for instance. The few methods that account for dependencies translate to sampling scenarios based on given marginals and dependence structures. However, for classes of decision-making problems based on robust, interval chance-constrained optimization, necessary inputs take the form of polyhedra or ellipsoids. Consequently, we propose a systematic framework to readily generate and evaluate ellipsoidal prediction regions, with predefined probability and minimum volume. A skill score is proposed for quantitative assessment of the quality of prediction ellipsoids. A set of experiments is used to illustrate the discrimination ability of the proposed scoring rule for misspecification of ellipsoidal prediction regions. Application results based on three datasets with wind, PV power and electricity prices, allow us to assess the skill of the resulting ellipsoidal prediction regions, in terms of calibration, sharpness and overall skill.Comment: 8 pages, 7 Figures, Submitted to IEEE Transactions on Power System

The Effect of Material Price and Product Demand Correlations on Combined Sourcing and Inventory Management

Both material sourcing and inventory management are important competitiveness factors, and it is a significant challenge to integrate the two areas. In sourcing, combined strategies using long-term contracts and the spot market received increasing attention recently, typically concentrating on the financial effects. However, there is limited research on the consequence of combined sourcing considering both purchasing and inventory effects from an operations point of view. In this paper, we analyze the effect of uncertainty on the combined sourcing decision under stochastic demand and random spot-market-price fluctuations and exploit the benefits of forward buying in periods with low spot-price realizations, but also of intended backordering in case of a high spot price. Since the decision on capacity reservation has to take into account the short-term utilization of each source which in turn depends on the available long-term contract capacity, decision making faces highly complex interactions between long-term and short-term decisions.From finance research, we find scarce evidence that the spot prices of commodities evolve independently over time. Rather, price correlation across time periods is found, and a popular way to describe these price dynamics is to model it as a mean reverting process. Thus, in this contribution we will respectively extend common i.i.d. price models from operations management studies and will additionally consider the effect of correlation between demand and price. In this paper, we provide a managerial analysis showing the effects of demand and spot market price correlations on the optimal procurement policy and provide managerial insights. We model the combined sourcing problem as a stochastic dynamic optimization problem and analyze the optimal procurement strategy by means of stochastic dynamic programming. The behavior of the optimal policy confirmed several previous assumptions, though some interesting and important managerial consequences arise due to demand and price correlations. Based on the policy analysis, a numerical study will reveal to which extent inobservance or misspecification of an existing level of correlation might result in performance losses in operational decision making. These observations play an important role under the trend of increasing volatility and dynamic changes on the spot market but also in the customer’s behavior

Optimization of Trading Physics Models of Markets

We describe an end-to-end real-time S&P futures trading system. Inner-shell stochastic nonlinear dynamic models are developed, and Canonical Momenta Indicators (CMI) are derived from a fitted Lagrangian used by outer-shell trading models dependent on these indicators. Recursive and adaptive optimization using Adaptive Simulated Annealing (ASA) is used for fitting parameters shared across these shells of dynamic and trading models

Risk evaluation with enhaced covariance matrix

We propose a route for the evaluation of risk based on a transformation of the covariance matrix. The approach uses a `potential' or `objective' function. This allows us to rescale data from different assets (or sources) such that each data set then has similar statistical properties in terms of their probability distributions. The method is tested using historical data from both the New York and Warsaw Stock Exchanges.Comment: see urbanowicz.org.p

Investment strategy due to the minimization of portfolio noise level by observations of coarse-grained entropy

Using a recently developed method of noise level estimation that makes use of properties of the coarse grained-entropy we have analyzed the noise level for the Dow Jones index and a few stocks from the New York Stock Exchange. We have found that the noise level ranges from 40 to 80 percent of the signal variance. The condition of a minimal noise level has been applied to construct optimal portfolios from selected shares. We show that implementation of a corresponding threshold investment strategy leads to positive returns for historical data.Comment: 6 pages, 1 figure, 1 table, Proceedings of the conference APFA4. See http://www.chaosandnoise.or