Paulo Renato A. Firmino

Correcting and combining time series forecasters

Combined forecasters have been in the vanguard of stochastic time series modeling. In this way it has been usual to suppose that each single model generates a residual or prediction error like a white noise. However, mostly because of disturbances not captured by each model, it is yet possible that such supposition is violated. The present paper introduces a two-step method for correcting and combining forecasting models. Firstly, the stochastic process underlying the bias of each predictive model is built according to a recursive ARIMA algorithm in order to achieve a white noise behavior. At each iteration of the algorithm the best ARIMA adjustment is determined according to a given information criterion (e.g. Akaike). Then, in the light of the corrected predictions, it is considered a maximum likelihood combined estimator. Applications involving single ARIMA and artificial neural networks models for Dow Jones Industrial Average Index, S&P500 Index, Google Stock Value, and Nasdaq Index series illustrate the usefulness of the proposed framework.

Error modeling approach to improve time series forecasters

Abstract In time series forecasting exercises it has been usual to suppose that the error series generated by the forecasters have a white noise behavior. However, it is possible that such supposition is violated in practice due to model misspecification or disturbances of the phenomenon not captured by the predictive models. It may lead to statistically biased and/or inefficient predictors. The present paper introduces an approach to correct predetermined forecasters by recursively modeling their remaining residuals. Two formalisms are used to illustrate the recursive approach: the well-known (linear) autoregressive integrated moving average (ARIMA) and the (non-linear) Artificial Neural Network (ANN). These models are recursively adjusted to the remaining residuals of a given forecaster until a white noise behavior is achieved. Applications involving ARIMA and ANN forecasters for Dow Jones Industrial Average Index, S&P500 Index, Google Stock Value, Nasdaq Index, Wolf׳s Sunspot, and Canadian Lynx data series indicate the usefulness of the proposed framework.

A Mixed Kijima Model Using the Weibull-Based Generalized Renewal Processes

Generalized Renewal Processes are useful for approaching the rejuvenation of dynamical systems resulting from planned or unplanned interventions. We present new perspectives for the Generalized Renewal Processes in general and for the Weibull-based Generalized Renewal Processes in particular. Disregarding from literature, we present a mixed Generalized Renewal Processes approach involving Kijima Type I and II models, allowing one to infer the impact of distinct interventions on the performance of the system under study. The first and second theoretical moments of this model are introduced as well as its maximum likelihood estimation and random sampling approaches. In order to illustrate the usefulness of the proposed Weibull-based Generalized Renewal Processes model, some real data sets involving improving, stable, and deteriorating systems are used.

Copulas-based time series combined forecasters

Time series combined forecasters have been superior to the respective single models in statistical terms. In this way, the linear combination functions, e.g. the simple average (SA) and the minimal variance (MV) approaches, have been the main alternatives for aggregation in the literature. In this work, it is presented a copulas-based method for combining biased single models. Copulas are multivariate functions that operate on marginal probability distributions and have the specific advantage of generalizing MV by flexibly modelling the forecasters residuals and then the dependence among them: a typical divide-and-conquer framework that can result in superior combined forecasters. The usefulness of the copulas-based combination method is highlighted by means of a comparison with SA and MV models, based on a number of simulated cases and a real-world time series.

Copulas-based ensemble of Artificial Neural Networks for forecasting real world time series.

Time series combined forecasters have been superior to the respective single models in statistical terms. In this way, the linear combination functions, e.g. the simple average (SA) and the minimal variance (MV) approaches, have been the main alternatives for aggregation in the literature. In this work, it is proposed a copulas-based method for combining biased single models. Copulas are multivariate functions that operate on marginal probability distributions, allowing one to model the forecasters errors and then the dependence among them: a typical divide-and-conquer framework that can result in nonlinear accurate combined forecasters. The performance of the copulas-based combination method is assessed by means of a comparison with SA and MV models, based on two financial time series.

Combining Time Series Forecasting Models via Gumbel-Hougaard Copulas

Researchers have been challenged to combine time series forecasting models, with the intention of enhancing forecast accuracy and efficiency. In this way, to weight models accuracy, efficiency, and mutual dependency becomes paramount. A promising way to address this issue is via copulas. Copulas are joint probability distribution functions aimed to envelop both the marginal distribution as well as the dependency among variables (e:g: forecasting models). This paper introduces copulas in the problem of combining time series forecasting models and proposes a maximum likelihood-based methodology in this context. Specifically, a Gumbel-Hougaard copulas model is presented. The usefulness of the resulting methodology is illustrated by means of simulated cases involving the combination of two single ARIMA models.

Combination of Biased Artificial Neural Network Forecasters

Artificial neural networks (ANN) have been paramount for modeling and forecasting time series phenomena. In this way it has been usual to suppose that each ANN model generates a white noise as prediction error. However, mostly because of disturbances not captured by each model, it is yet possible that such supposition is violated. On the other hand, to adopt a single ANN model may lead to statistical bias and underestimation of uncertainty. The present paper introduces a two-step maximum likelihood method for correcting and combining ANN models. Applications involving single ANN models for Dow Jones Industrial Average Index and S&P500 series illustrate the usefulness of the proposed framework.

Mapa estratégico para programas de recursos humanos: avaliando o desempenho de redes Bayesianas

Visando desenvolver mao de obra especializada na area de petroleo, gas natural e biocombustiveis, a Agencia Nacional do Petroleo - ANP - tem promovido programas de capacitacao de Recursos Humanos (PRH) em todo o Pais. Com o objetivo de elaborar as estrategias subjacentes a tais programas de maneira estruturada e abrangente, metodos de administracao tais como Balanced Scorecard (BSC) vem sendo adotados. Contudo, infortunios como a nao mensuracao das incertezas envolvidas ate o alcance dos objetivos almejados sugerem a adocao de formalismos mais sofisticados, tais como redes Bayesianas (RB), em detrimento da BSC. Em se tratando de RBs, o desafio passa a ser uma quantificacao adequada dos seus parâmetros, possibilitando estimativas confiaveis a partir delas. O objetivo do presente trabalho e avaliar o desempenho de RBs no suporte a um dado problema real de PRH, a partir do confronto entre seus prognosticos e o que foi de fato observado. O modelo em questao foi elaborado a partir de um BSC e posteriormente quantificado de acordo com opinioes de especialistas, devido a total ausencia de dados empiricos relevantes. A RB foi delineada para dar suporte a definicao e implantacao de estrategias para o desenvolvimento cientifico e abertura de mercados especializados para dado curso de engenharia de uma universidade federal do Pais. As analises realizadas indicam o bom desempenho do modelo e apontam como um dos principais componentes responsaveis o metodo de quantificacao adotado.

Optical monitoring system availability optimization via semi-Markov processes and genetic algorithms

System availability optimization is one of the main issues to oil production managers: the greater the system availability the greater the production profits are. Provided that preventive maintenance actions promote rejuvenation impact on availability indicator, this paper proposes an approach to maximize the mean availability by identifying an optimal maintenance policy for downhole optical monitoring systems, which are modeled according to non-homogeneous semi-Markov processes. In order to solve the resulting optimization problem constrained by system performance costs, new real-coded GA operators are also presented. The proposed approach is exemplified by means of an application to a real scenario in onshore oil wells in Brazil.

DEFENSE-ATTACK INTERACTION OVER OPTIMALLY DESIGNED DEFENSE SYSTEMS VIA GAMES AND RELIABILITY

This paper analyzes defense systems taking into account the strategic interactions between two rational agents; one of them is interested in designing a defense system against purposeful attacks of the other. The interaction is characterized by a sequential game with perfect and complete information. Reliability plays a fundamental role in both defining agents actions and in measuring performance of the defense system for which a series-parallel configuration is set up by the defender. The attacker, in turn, focuses on only one defense subsystem in order to maximize her efficiency in attacking. An algorithm involving backward induction is developed to determine the equilibrium paths of the game. Application examples are also provided.