Abstract: The problem of identifying similarities or dissimilarities in time series data has been studied for some time in the discrimination and clustering literature. Many studies have used metrics based on contemporaneous or quasi-contemporaneous correlations between different time series. Other studies have used nonparametric approaches for splitting a set of time series into different clusters.
We have been working on measures that aim to group time series according to their stochastic properties, independently of their co-movements. We introduced autocorrelation and periodogram measures. Later, we extended the periodogram similarity measures to the case of time series with different lengths. We present some examples showing how these methods can deal with financial and economic time series (This presentation includes some joint work with Jorge Caiado, Instituto Politécnico de Setúbal, and Daniel Peña, Universidad Carlos III de Madrid.)
Abstract: The Shewhart control charts, used for monitoring industrial processes, are the most popular tools in Statistical Process Control (SPC). They are usually developed under the assumption of independent and normally distributed data, an assumption rarely true in practice, and are usually implemented with estimated control limits. Despite the advantages of the use of the normal distribution in SPC, it is well known that most of the datasets from diversified industrial processes (such as data from telecommunication traffic, insurance, finance and reliability) exhibit often asymmetry and tails heavier than the normal tail. As in general we mainly want to control the process mean value and the process standard deviation, independently of the data distribution, to monitor these process parameters it seems sensible to advance with control charts based on robust statistics, because these statistics are expected to be more resistant to moderate changes in the underlying process distribution.
In this talk we introduce some background about the total median and the total range statistics, and we present a simulation study on their robustness and efficiency. Then, apart from the traditional control charts, the sample mean and the sample range charts, we consider control charts based on the total median and on the total range statistics for monitoring a cork stopper’s process production. These charts are compared in terms of robustness and performance. (This presentation is a joint work with Maria Ivette Gomes, Universidade de Lisboa, F.C.U.L. (D.E.I.O.) and C.E.A.U.L.).
Abstract: This talk is based upon work with several co-authors, see Gaspar and Murgoci (2008) and Gaminha, Gaspar and Oliveira (2009). It aims to clarify the notion of convexity in fixed income markets. The basic and appealing idea behind the use of convexity adjustments is presented focusing the situations that are of particular importance to practitioners: yield convexity adjustments, forward versus futures convexity adjustments, timing and quanto convexity adjustments (more info).
Abstract: In 1695 L'Hopital wrote a letter to Leibniz asking for the meaning of Dny for n = 1/2. Leibniz replied 'It seems that useful consequences shall be drawn from these paradoxes one day, as there are no paradoxes that do not prove useful'. The term 'Fractional Calculus' (FC) was adopted at that time and is used even nowadays, although many researchers find more adequate the terminology 'integration and differentiation of arbitrary order'. Starting with the ideas of Leibniz many important mathematicians developed the theoretical concepts, but practical aspects were not evident. During the thirties A. Gemant and O. Heaviside applied FC in the areas of mechanical and electrical engineering, respectively. Nevertheless, these important contributions were somehow forgotten and only during the eighties, we find relevant work, by A. Oustaloup, that developed a pioneering work in the FC application in automatic control systems. In the same period, FC emerged as an important tool associated with phenomena such as fractal and chaos and, consequently, in the modeling of dynamical systems. The ongoing research of FC application addresses many different aspects such as viscoelasticity and damping, biology, electronics, signal processing, system identification, diffusion and wave propagation, percolation, modeling, identification, and control. Bearing these ideas in mind, this lecture introduces the FC fundamental mathematical aspects and discuses some of their consequences. Based on the FC concepts, the lecture reviews the main approaches for implementing fractional operators. Finally are presented some applications in engineering, namely the fractional PID controller, heat diffusion systems, electromagnetism, fractional electrical impedances, and nonlinear systems.
Abstract: Supervised training implies the tuning of parameters in a model so that its output may match a training set and the model may generalize for other cases. Least squares or minimum square error (MSE) is a criterion with generalized use in engineering and in many cases it is applied without questioning the soundness of this choice - however, this is only an optimal chioce if the error distribution is Gaussian.
Wins power forecasting is a difficult exercise with important industrial application that has become a good practical example of the advantage of abandoning the MSE paradigm. Departing from the challenge of predicting wind power on a 3-day ahead schedule, one will demonstrate, with practical examples, that criteria associated with the entropy of the error distributionn allow the industry to obtain better predictions and thus save or make money in the power business.
The application to neural networks will be described and other areas of application suggested. Cases tested at INESC Porto will be presented..
Abstract: We describe three different but related scenarios for the determination of contingent claims prices in an incomplete market: one scenario uses a market game approach whereas the other two are based on risk sharing or regret minimizing considerations. Furthermore, we point out some dynamical schemes modelling the convergence of the buyer's and of the seller's prices of a given asset to a unique price.
Abstract: Improving the use of resources, such as materials, space and time, is a relevant contribution to increase productivity, to reduce costs and to convey a better public image. Several industries such as textile, garment, electronic, leather and shoes, paper, metal, wood and furniture and glass industry need an everyday plan of patterns or layouts, associated with the objects or pieces of different shapes to cut or pack, in order to save expensive materials, to achieve a good usage of space and to ease the production and cutting tools procedures.The presentation starts by describing the context of these situations and problems and will be supported by real applications.Convenient Optimisation models and Graphs models will be presented and discussed.Resolution approaches based on Mathematical Programming techniques (Linear and Integer Optimisation) and Meta-heuristics will also be outlined. Emphasis is placed on Metaheuristics methods, such as Simulated Annealing, Genetic Algorithms, Memetic Algorithms and Tabu Search, due to their novelty and generality.
Abstract: In this talk we review, in broad and nontechnical terms, a number of features and properties of optimization problems which appear frequently in industrial and computational science applications.