7 research outputs found

    Time series forecasting with the WARIMAX-GARCH method

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    It is well-known that causal forecasting methods that include appropriately chosen Exogenous Variables (EVs) very often present improved forecasting performances over univariate methods. However, in practice, EVs are usually difficult to obtain and in many cases are not available at all. In this paper, a new causal forecasting approach, called Wavelet Auto-Regressive Integrated Moving Average with eXogenous variables and Generalized Auto-Regressive Conditional Heteroscedasticity (WARIMAX-GARCH) method, is proposed to improve predictive performance and accuracy but also to address, at least in part, the problem of unavailable EVs. Basically, the WARIMAX-GARCH method obtains Wavelet “EVs” (WEVs) from Auto-Regressive Integrated Moving Average with eXogenous variables and Generalized Auto-Regressive Conditional Heteroscedasticity (ARIMAX-GARCH) models applied to Wavelet Components (WCs) that are initially determined from the underlying time series. The WEVs are, in fact, treated by the WARIMAX-GARCH method as if they were conventional EVs. Similarly to GARCH and ARIMA-GARCH models, the WARIMAX-GARCH method is suitable for time series exhibiting non-linear characteristics such as conditional variance that depends on past values of observed data. However, unlike those, it can explicitly model frequency domain patterns in the series to help improve predictive performance. An application to a daily time series of dam displacement in Brazil shows the WARIMAX-GARCH method to remarkably outperform the ARIMA-GARCH method, as well as the (multi-layer perceptron) Artificial Neural Network (ANN) and its wavelet version referred to as Wavelet Artificial Neural Network (WANN) as in [1], on statistical measures for both in-sample and out-of-sample forecasting

    Método warimax-garch neural para previsão de séries temporais

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    Orientador : Prof. Dr. Anselmo Chaves NetoCo-orientador : Prof. Dr. Luiz Albino Teixeira JúniorTese (doutorado) - Universidade Federal do Paraná, Setor de Tecnologia, Programa de Pós-Graduação em Métodos Numéricos em Engenharia. Defesa: Curitiba, 21/12/2015Inclui referências : f.123-128Área de concentração: Programação matemáticaResumo: A proposta deste trabalho é apresentar uma nova metodologia híbrida WARIMAX-GARCH Neural para a previsão pontual e intervalar de séries temporais estocásticas. Fundamentalmente, é aplicada a decomposição Wavelet em séries históricas compostas por registros de monitoramento de barragens e suas componentes de aproximação e detalhe, as quais são modeladas, individualmente, via ARIMA-GARCH e Redes Neurais Artificiais (RNA). A partir de então, são realizadas as previsões pontuais fora da amostra pelas técnicas de modelagem e os resultados são combinados linearmente. As componentes de aproximação e detalhe são completadas com as previsões combinadas e passam a ser utilizadas como variáveis de entrada (exógenas híbridas) na modelagem da série em estudo. Em cada série temporal é aplicada a metodologia WARIMAX-GARCH Neural e são realizadas as previsões pontuais e intervalares, sob a suposição de inovações gaussianas. As séries temporais utilizadas neste trabalho de tese foram as séries temporais dos deslocamentos horizontais de blocos da barragem principal da Usina Hidrelétrica de Itaipu, aferidas pelos pêndulos diretos automatizados. Os desempenhos preditivos alcançados pela metodologia proposta, em relação aos resultados obtidos pelas modelagens tradicionais ARIMA-GARCH e RNA, foram consideravelmente vantajosos. Nas comparações dos resultados obtidos através do modelo WARIMAX-GARCH Neural com métodos tradicionais, a redução do erro preditivo chegou a 91%. Palavras-chave: Monitoramento de Barragens, Previsão de Séries Temporais, Modelos ARIMA, Modelos GARCH, Redes Neurais Artificiais, Decomposição Wavelet.Abstract: This research proposes a new WARIMAX-GARCH Neural hybrid methodology for point and interval prediction of stochastic time series. Fundamentally, it is applied the wavelet decomposition on the time series made of monitoring data and its approximation and detail components were modeled by ARIMA-GARCH and Artificial Neural Networks (ANN). Thereafter, the point forecasts are performed out the sample by both modeling techniques and these results are combined linearly. The approximation and detail components are completed with the combined forecasts and are used as input variables (hybrid exogenous) in the modeling time series under study. In each time series is applied the WARIMAX-GARCH Neural methodology and are made the point and interval forecast, under the assumption of Gaussian innovations. The time series used in this research were the time series of horizontal displacements of the main dam blocks of Itaipu hydroelectric plant, measured by automated direct pendulums. The predictive performances achieved by the proposed method compared to the results obtained by traditional modeling ARIMA-GARCH and RNA were considerably advantageous. Comparing the results obtained by WARIMAX-GARCH Neural model to traditional methods there was a reduction of up to 91% of the predictive error. Keywords: Dams Monitoring, Forecast Time Series, ARIMA Models, GARCH Models, Artificial Neural Networks, Wavelet Decomposition

    Прогнозирование рядов динамики рыночных индикаторов на основе нелинейной авторегрессионной нейронной сети

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    The modern practice of economic research relies heavily on mathematical models that make it possible to reveal hidden regularities in statistical data and make forecasts on their basis. Linear models based on vector autoregression (VAR) are the most common. However, the relationship between time series in the economy is often difficult to identify, so non-linear autoregressive (NAR) models show more reliable results. Artificial neural networks (ANNs) are usually used for implementation of these models, but ANNs do not provide the possibility of estimating the forecast in the form of mathematical expectation and a standard deviation. Therefore, the model proposed in the article combines two blocks: VAR and NAR. NAR is used to construct a prediction for a given number of points, and VAR for estimating the forecast in the form of a mathematical expectation and a standard deviation. The evaluation of the model was carried out on the daily data: exchange rate USD / RUB and “Brent” oil from 1.01.2016 to 1.03.2017. The average accuracy of forecasting the trend for the dollar was 54.9%, for the oil prices it was 54.0%. In this case, the relative error in predicting the dollar rate was from 1.09% (for the first point) to 2.01% (for the tenth point); the relative error in forecasting oil prices was from 1.28% (for the first point) to 4.58 % (for the tenth point). Thus, the model showed accurate results when predicting dynamic series and can be used to solve other forecasting problems. In particular, it is expedient to use the model as one of the factors when making investment decisions. In addition, the evaluation of forecasts is done on the basis of testing the NAR block of historical data and on the basis of VAR block forecast in the form of mathematical expectation and standard deviation.Современная практика экономических исследований активно полагается на математические модели, позволяющие выявлять в статистических данных скрытые закономерности и строить на их основании прогнозы. Линейные модели прогнозирования рядов динамики, основанные на векторной авторегрессии (VAR) являются наиболее распространенными. Однако связи между рядами динамики в экономике часто имеют сложно идентифицируемый характер, поэтому нелинейные авторегрессионные (NAR) модели показывают более достоверные результаты. Для их реализации обычно используются нейронные сети, которые не предоставляют возможности оценки прогноза в виде математического ожидания и стандартного отклонения. Поэтому предлагаемая в статье модель сочетает в себе два блока: VAR и NAR. NAR используется для построения прогноза на заданное количество точек, а VAR для оценки прогноза в виде математического ожидания и стандартного отклонения. Оценка достоверности модели проводилась на дневных данных валютного курса USD/RUB и цен на нефть марки «Брент» с 1.01.2016 по 1.03.2017. Средняя точность прогнозирования тренда для курса доллара США к рублю составила 54,9%, для цены нефти – 54,0%. При этом относительная ошибка прогнозирования курса доллара составила от 1,09% (для первой точки) до 2,01% (для десятой точки), относительная ошибка прогнозирования цен на нефть составила от 1,28% (для первой точки) до 4,58% (для десятой точки). Таким образом, модель представляет достаточно точные для принятия инвестиционных решений прогнозы, при этом производится оценка прогнозов на основании тестирования NAR блока на исторических данных и на основании прогноза VAR блока в форме математического ожидания и стандартного отклонения

    Day-ahead forecasting approach for energy consumption of an office building using support vector machines

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    This paper presents a Support Vector Machine (SVM) based approach for energy consumption forecasting. The proposed approach includes the combination of both the historic log of past consumption data and the history of contextual information. By combining variables that influence the electrical energy consumption, such as the temperature, luminosity, seasonality, with the log of consumption data, it is possible for the proposed method by find patterns and correlations between the different sources of data and therefore improves the forecasting performance. A case study based on real data from a pilot microgrid located at the GECAD campus in the Polytechnic of Porto is presented. Data from the pilot buildings are used, and the results are compared to those achieved by several states of the art forecasting approaches. Results show that the proposed method can reach lower forecasting errors than the other considered methods.This work has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 641794 (project DREAM-GO) and from FEDER Funds through COMPETE program and from National Funds through FCT under the project UID/EEA/00760/2013info:eu-repo/semantics/publishedVersio

    Previsão das séries temporais dos deslocamentos horizontais dos blocos da Barragem de Itaipu por meio de redes neurais recorrentes do tipo LSTM

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    Orientador: Prof. Dr. Jairo Marlon Corrêa.Coorientador: Prof. Dr. Anselmo Chaves Neto.Coorientador: Prof. Dr. Samuel Bellido Rodrigues.Convênio UFPR/UNILA.Monografia (especialização) - Universidade Federal do Paraná, Setor de Tecnologia e Setor de Ciências Exatas, Curso de Especialização em Métodos Numéricos em Engenharia.Inclui referênciasResumo : O monitoramento da saúde estrutural da barragem é um dos assuntos de maior importância no âmbito da segurança das mesmas. Dados como temperatura, deslocamento, nível da água são vitais para o correto planejamento dos trabalhos de manutenção. Neste trabalho foram obtidas as previsões dos dados de deslocamento horizontal dos blocos F05, F13, e F19 nos eixos X (na direção do fluxo do rio) e Y (perpendicular ao fluxo do rio), obtidos pelos pêndulos diretos instalados na estrutura da Usina Hidrelétrica da Itaipu Binacional por meio do uso de redes neurais artificiais recorrentes do tipo Long Short Term Memory (LSTM). Este tipo de redes permite melhor utilização dos dados passados para a previsão, devido a seu caráter recorrente e o uso de células de memória. Com isto, um modelo foi proposto com uma busca por grade para refinar melhor os hiperparâmetros. Os resultados obtidos demonstram a eficiência da técnica quando utilizada nas referidas séries temporais quando comparada com técnicas como ARIMA e Redes Neurais MLP. Finalmente, pode-se concluir que as redes neurais recorrentes são promissoras para a área de previsões das séries temporais e o modelo proposto deve ser testado em mais dados de séries temporais.Abstract : The monitoring of the structural health of the dam is one of the most critical issues in dam safety. Data such as temperature, displacements, water level, among others are vital to the correct planning of maintenance. In this work, data from direct pendulums installed inside Itaipu Hydroelectric Power Plant is used to forecast horizontal displacement of F05, F13 and F19 blocks in the X-axes (in the direction of river flow) and Y-axes (perpendicular to river flow) with recurrent neural networks of the type Long Short Term Memory (LSTM). This type of network allows better use of the data due to its recurrent character and the use of memory cells. A model architecture was proposed with a grid search to tune its hyperparameters. The forecast results demonstrate the efficiency of the technique for these particular time series when compared to ARIMA and MLP. Finally, we conclude that using recurrent neural networks for time series is promising, and the proposed model should be tested with more time series data

    Modelagem e previsão de deslocamentos em barragens de concreto : aplicação a dados de instrumentação da Usina Hidrelétrica de Itaipu

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    Orientador : Prof. Dr. Anselmo Chaves NetoTese (doutorado) - Universidade Federal do Paraná, Setor de Tecnologia, Programa de Pós-Graduação em Métodos Numéricos em Engenharia. Defesa: Curitiba, 03/06/2016Inclui referências : f. 93-97Área de concentraçãoResumo: Neste trabalho propõe-se uma nova metodologia de previsão para os deslocamentos de um bloco de concreto de uma barragem baseada nas séries históricas dos instrumentos pêndulos direto e invertido instalados no bloco. O método desenvolvido foi aplicado à Barragem de Itaipu. Características dos dados registrados, tais como a autocorrelação, a multicolinearidade e a presença de séries temporais integradas de diferentes ordens foram determinantes para o delineamento da metodologia. A metodologia proposta consiste em ajustar modelos Autorregressivos de Defasagens Distribuídas (ADL) para aplicar a abordagem Bounds Testing e assim modelar os deslocamentos horizontais de um bloco de concreto, validar os modelos, realizar as previsões para um horizonte além do observado e construir intervalos de confiança para essas previsões. Os modelos propostos, que são o Modelo de Correção de Erros (ECM) Irrestrito e o Restrito, serão comparados a modelos estatísticos clássicos, tais como modelos Autorregressivos Integrados Médias Móveis (ARIMA) e modelos de Vetores Autorregressivos (VAR). A comparação foi realizada por meio de medidas de avaliação do erro das previsões fora da amostra e avaliação dos gráficos das previsões. Um dos modelos propostos, o ECM irrestrito, apresentou menores medidas de avaliação de erro e o desempenho foi satisfatório na avaliação dos gráficos das previsões fora da amostra. Para cada sensor do pêndulo, foram construídos intervalos de confiança para as previsões do modelo ECM irrestrito, estabelecendo novos limites para as observações de deslocamentos. A metodologia apresentada possui uma configuração inovadora e assim um novo modelo de previsão é inserido na área de monitoramento de barragens de concreto. Palavras-chave: Monitoramento de Barragens. ADL. Modelo de Correção de Erros. Bounds Testing. Previsão. Deslocamentos.Abstract: This work proposes a new methodology for forecasting the displacement of a concrete block of a dam based on historical series of direct and inverted pendulum installed in the block. The developed method was applied to the Itaipu Dam. Characteristics of recorded data such as the autocorrelation, multicollinearity and the presence of integrated time series of different orders were decisive for the design of the methodology. The proposed methodology consists of: adjusting Autoregressive Distributed Lag models (ADL) and apply the Bounds Testing approach, and thus, modeling the horizontal displacements of a concrete block, validate the models, make forecasts for a horizon beyond the observed and build confidence intervals for these forecasts. The proposed models, which are the Error Correction Model (ECM) Unrestricted and Restricted, will be compared to classic statistical models such as Autoregressive Integrated Moving Average models (ARIMA) and Autoregressive Vectors (VAR). The comparison was performed by evaluation of measurements error of forecasts out-of-sample and evaluation of the graphs of forecasts. One of the proposed models, the unrestricted ECM, showed lower error evaluation measures and its performance was satisfactory in the evaluation of the graphs of out-of-sample forecasts. For each pendulum sensor, confidence intervals were constructed for the predictions of the ECM unrestricted model, setting new limits for observations of displacement. This methodology has an innovative configuration and thus a new forecasting model is inserted into the monitoring field of concrete dams. Keywords: Monitoring Dams. ADL. Error Correction Model. Bounds Testing. Forecast. Displacements
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