In today's world the amount of collected data increases every day, this is a trend which is likely to continue. At the same time the potential value of the data does also increase due to the constant development and improvement of hardware and software. However, in order to gain insights, make decisions or train accurate machine learning models we want to ensure that the data we collect is of good quality. There are many definitions of data quality, in this thesis we focus on the accuracy aspect. One method which can be used to ensure accurate data is to monitor for and alert on anomalies. In this thesis we therefore suggest a method which, based on historic values, is able to detect anomalies in time series as new values arrive. The method consists of two parts, forecasting the next value in the time series using Holt-Winters method and comparing the residual to an estimated Gaussian distribution. The suggested method is evaluated in two steps. First, we evaluate the forecast accuracy for Holt-Winters method using different input sizes. In the second step we evaluate the performance of the anomaly detector when using different methods to estimate the variance of the distribution of the residuals. The results indicate that the suggested method works well most of the time for detection of point anomalies in seasonal and trending time series data. The thesis also discusses some potential next steps which are likely to further improve the performance of this method. / I dagens värld ökar mängden insamlade data för varje dag som går, detta är en trend som sannolikt kommer att fortsätta. Samtidigt ökar även det potentiella värdet av denna data tack vare ständig utveckling och förbättring utav både hårdvara och mjukvara. För att utnyttja de stora mängder insamlade data till att skapa insikter, ta beslut eller träna noggranna maskininlärningsmodeller vill vi försäkra oss om att vår data är av god kvalité. Det finns många definitioner utav datakvalité, i denna rapport fokuserar vi på noggrannhetsaspekten. En metod som kan användas för att säkerställa att data är av god kvalité är att övervaka inkommande data och larma när anomalier påträffas. Vi föreslår därför i denna rapport en metod som, baserat på historiska data, kan detektera anomalier i tidsserier när nya värden anländer. Den föreslagna metoden består utav två delar, dels att förutsäga nästa värde i tidsserien genom Holt-Winters metod samt att jämföra residualen med en estimerad normalfördelning. Vi utvärderar den föreslagna metoden i två steg. Först utvärderas noggrannheten av de, utav Holt-Winters metod, förutsagda punkterna för olika storlekar på indata. I det andra steget utvärderas prestandan av anomalidetektorn när olika metoder för att estimera variansen av residualernas distribution används. Resultaten indikerar att den föreslagna metoden i de flesta fall fungerar bra för detektering utav punktanomalier i tidsserier med en trend- och säsongskomponent. I rapporten diskuteras även möjliga åtgärder vilka sannolikt skulle förbättra prestandan hos den föreslagna metoden.

[pt] Após o choque de racionamento de energia elétrica, decorrente do desequilíbrio entre oferta e demanda, os vários setores da sociedade brasileira constataram a real e iminente necessidade de diversificação das fontes de geração de energia elétrica e de seu uso racional. Busca-se hoje novas fontes, entre as quais a energia eólica, uma alternativa nova e promissora. A energia eólica está aumentando no mundo todo e o Brasil tem um enorme potencial devido a sua localização geográfica e o governo tem investido neste tipo de energia. O principal objetivo desta dissertação é estudar e desenvolver modelos de previsão de velocidade de vento, de curto prazo da velocidade do vento. Os métodos de amortecimento exponencial, em particular o método de Holt-Winters e suas variações, são apropriados para este contexto devido à sua alta adaptabilidade e robustez. Para aplicação da metodologia considerou-se o município de São João do Cariri (Estado de Paraíba), onde está localizada uma das estações de referência do projeto SONDA (Sistema Nacional de Dados Ambientais para o setor de energia). Será utilizado o método de Holt-Winters, que será comparado com os modelos: de persistência, neuro-fuzzy (ANFIS) e estatísticos. / [en] After the shock of electricity rationing, due to the imbalance between supply and demand, the various sectors of the Brazilian society found a real and imminent need to diversify sources of electricity generation and its rational use. New sources are searched today, including wind power, a promising new alternative. Wind energy has been increasing worldwide and Brazil has huge potential due to its geographical location and the government has invested in this type of energy. The main objective of this thesis is to study and develop forecasting models, of short-term wind speed. The methods of exponential smoothing, in particular the method Holt-Winters and its variations, are suitable in this context because of its high adaptability and robustness. The city of São João do Cariri (State of Paraíba), where it is located one of the reference stations of project SONDA (National Environmental Data for the energy sector) was chosen in order to apply the methodology. The method that will be used is Holt-Winters, who will be compared with the models: persistence, neuro-fuzzy (ANFIS) and statistics.

Title: Methods for periodic and irregular time series Author: Mgr. Tomáš Hanzák Department: Department of Probability and Mathematical Statistics Supervisor: Prof. RNDr. Tomáš Cipra, DrSc. Abstract: The thesis primarily deals with modifications of exponential smoothing type methods for univariate time series with periodicity and/or certain types of irregularities. A modified Holt method for irregular times series robust to the problem of "time-close" observations is suggested. The general concept of seasonality modeling is introduced into Holt-Winters method including a linear interpolation of seasonal indices and usage of trigonometric functions as special cases (the both methods are applicable for irregular observations). The DLS estimation of linear trend with seasonal dummies is investigated and compared with the additive Holt-Winters method. An autocorrelated term is introduced as an additional component in the time series decomposition. The suggested methods are compared with the classical ones using real data examples and/or simulation studies. Keywords: Discounted Least Squares, Exponential smoothing, Holt-Winters method, Irregular observations, Time series periodicity

[pt] O objetivo do presente trabalho é o desenvolvimento de um algoritmo estatístico de previsão da potência transmitida pela usina geradora termelétrica de Linhares, localizada no Espírito Santo, medida no ponto de entrada da rede da concessionária regional, a ser integrado em plataforma composta por sistema supervisório em tempo real em ambiente MS Windows. Para tal foram comparadas as metodologias de Modelos Arima(p,d,q), regressão usando polinômios ortogonais e técnicas de amortecimento exponencial para identificar a mais adequada para a realização de previsões 5 passos-à-frente. Os dados utilizados são provenientes de observações registradas a cada 5 minutos, contudo, o alvo é produzir estas previsões para observações registradas a cada 5 segundos. Os resíduos estimados do modelo ajustado foram analisados via gráficos de controle para checar a estabilidade do processo. As previsões produzidas serão usadas para subsidiar decisões dos operadores da usina, em tempo real, de forma a evitar a ultrapassagem do limite de 200.000 kW por mais de quinze minutos. / [en] The objective of this study is to develop a statistical algorithm to predict the power transmitted by a thermoelectric power plant in Linhares, located at Espírito Santo state, measured at the entrance of the utility regional grid, which will be integrated to a platform formed by a real time supervisor system developed in MS Windows. To this end we compared Arima (p,d,q), Regression using Orthogonal Polynomials and Exponential Smoothing techniques to identify the best suited approach to make predictions five steps ahead. The data used are observations recorded every 5 minutes, however, the target is to produce these forecasts for observations recorded in every five seconds. The estimated residuals of the fitted model were analysed via control charts to check on the stability of the process. The forecasts produced by this model will be used to help not to exceed the 200.000 kW energy generation upper bound for more than fifteen minutes.