Background Forecasts are used as a basis for decision making and they mainly affect decisions at strategic and tactical levels in a company or organization. There are two different methods to perform forecasts. The first one is a qualitative method where a n expert or group of experts tell about the future. The second one is a quantitative method where forecast are produced by mathematical and statistical models. This study used a quantitative method to build a forecast model and took into account external f actors in forecasting the sales volume of Bosch Rexroth’s hydraulic motors. There is a very wide range of external factors and only a limited selection had been analyzed in this study. The selection of the variables was based on the markets where Bosch Rexroth products are used, such as mining. Purpose This study aimed to develop five predictive models: one model for the global sales volume, one model each for sales volume in USA and China and one model each for sales volume of CA engine and Viking engine. By identifying external factors that showed significant relationship in various time lags with Bosch Rexroth’s sales volume, the forecasts 2016 and 2017 were produced. Methods The study used a combination of multiple linear regression and a Box - Jenkins AR MA errors to analyze the association of external factors and to produce forecasts. Externa l factors such as commodity prices, inflation and exchange rates between different currencies were taken into account. By using a cross - correlation function between external factors and the sales volume, significant external factors in different time lags were identified and then put into the model. The forecasting method used is a Causal forecasting model. Conclusions The global sales volume of Bosch Rexroth turned out to be affected by the historical price of copper in three different time lags , one, six and seven months . From 2010 to 2015, the copper price have been continuously dropping which explain s the downward trend of the sales volume. The sales volume in The U SA showed a significant association by the price of coal with three and four time lags. This means that the change of coal price takes three and four months before it affects the sales volume in the USA. The market in China showed to be affected by the development of the price of silver. The volume of sales is affected by the price of silver by four and six time lags. CA engine also displayed association with the price of copper at the same time lags as in the global sales volume. On the other hand, Viking engine showed no significant association at all with any of the external factors that were analyzed in this study. The forecast for global mean sales volume will be between 253 to 309 units a month for May 2016 – December 2017. Mean sales volume in USA projected to be in between 24 to 32 units per month. China's mean sales volume is expected to be in between 42 to 81 units a month. Mean sales volume of CA engine has a forecast of 175 to 212 units a month. While the mean s ales of Viking engine projected to stay in a constant volume of 25 units per month.

This thesis deals with comparing two approaches to modelling and predicting time series: a traditional one (the ARIMAX model) and a modern one (gradiently boosted decision trees within the framework of the XGBoost library). In the first part of the thesis we introduce the theoretical framework of supervised learning, the ARIMAX model and gradient boosting in the context of decision trees. In the second part we fit the ARIMAX and XGBoost models which both predict a specific time series, the daily volume of the S&P 500 index, which is a crucial task in many branches. After that we compare the results of the two approaches, we describe the advantages of the XGBoost model, which presumably lead to its better results in this specific simulation study and we show the importance of hyperparameter optimization. Afterwards, we compare the practicality of the methods, especially in regards to their computational demands. In the last part of the thesis, a hybrid model theory is derived and algorithms to get the optimal hybrid model are proposed. These algorithms are then used for the mentioned prediction problem. The optimal hybrid model combines ARIMAX and XGBoost models and performs better than each of the individual models on its own. 1

In this thesis we investigate whether the inclusion of an exogenous variable in the form of patentapproval can improve the ARIMA model's predictions for the pharmaceutical companyAstrazeneca. A point of departure for the study is the questioning of the efficient markethypothesis. When comparing data on patent date approval with stock exchange data for threepharmaceutical companies, it could be observed that share prices increased on the date ofapproval in 65 percent of the cases. This observed correlation combined with the fact that severalpapers have established that the stock market may not be efficient make it interesting to studywhether the value of a patent has been included in the stock price prior to approval date.To investigate this, an ARIMA and an ARIMAX model was estimated. The exogenous variable,which controls for patent approvals, was created by retrieving data from the EPO's databasePATSTAT. The retrieved data was then formatted into a dummy variable. The purpose ofincluding an exogenous variable is to investigate whether the market reacts to patent information.If the addition of the exogenous variable proves significant, the result is in conflict with theefficient market hypothesis.During the model selection, it was found that an ARIMA (4,1,2) was the superior model. Themodel was then compared with the corresponding ARIMAX model. When comparing themodels, it was found that the predictions of the ARIMAX model follow the observed datasomewhat better, but a t-test concluded that the improvement was not statistically significant.This implies that the value of the patent has already been included in stock prices prior to patentapproval and indicates that the price increase is random. This results thus lends support for theefficient market hypothesis. To investigate this further, the stock market data was compared witha random walk and by conducting a t-test it could be concluded that it was not possible to rejectthe hypothesis that share prices follow a random walk, thus the result further supports theefficient market hypothesis.

[pt] Adequação e validação de métodos econométricos para quantificar o impacto da padronização (normalização) de produtos no consumo e no bem estar dos consumidores. Três são os objetivos centrais da presente pesquisa: (i) caracterização do impacto da implementação da padronização na produção de açúcar, (ii) desenvolvimento de metodologia para a quantificação do impacto da implementação da padronização (normalização de pré-medidos) sobre o nível de produção e, portanto, sobre o bem-estar dos consumidores e (iii) análise do acervo de normas e regulamentação técnica aplicável ao setor açucareiro. Como motivação o trabalho mostra que funções da tecnologia industrial básica constituem de fato instrumentos de redução da assimetria da informação. O trabalho se desenvolveu no recente contexto de implementação de políticas públicas sociais que visam à melhoria do bem-estar de consumidores de baixa renda. O trabalho se desenvolveu em conformidade aos seguintes preceitos metodológicos: (i) revisão da literatura relacionada à assimetria da informação com o propósito de comprovar a hipótese de que a padronização de produtos pode de fato reduzir a assimetria informação; (ii) análise econométrica das sérias históricas da produção brasileira de açúcar. Os resultados do trabalho mostraram que a padronização do açúcar (normalização de pré-medidos), se devidamente implementada, pode implicar na melhoria no bem estar dos consumidores. Uma análise contra-factual clássica dos resultados consolidados mostrou que a padronização brasileira do açúcar reduziu a assimetria da informação presenciada nesse mercado, impactando num aumento de cerca de 8 porcento na produção de açúcar em 2006 devido `a padronização do produto implementada em 1992. Como conclusão a análise econométrica permitiu mostrar que a padronização de produtos constitui-se numa ferramenta estratégica a serviço do Estado promover a competitividade e como instrumento de redução de assimetria da informação em benefício do consumidor e de redução de distorções de mercados. / [en] There are two objetives in this Master dissertation in Metrology: (i) characterization of the impact of the implementation of the standardization in the production of sugar and (ii) development of methodology for quantifying the impact of the implementation of the standardization on the production level and, therefore, on the welfare of consumers. The work was motivated by the use of functions of basic industrial technology to reduce the asymmetric information as market failure is able to generate deficiencies. The investigation was developed in the recent context characterized by the implementation of social public policies aimed to improve the low income consumer s welfare. The work was developed in accordance to the following methodological precepts: (i) review of the literature on asymmetric information in order to verify the hypothesis that the products standardization can reduce the asymmetric information, generating an improvement in the consumer s welfare; (ii) econometric analysis of the Brazilian sugar production time series. As a result, the research shows that the sugar standardization, if correctly implemented, induces consumer s welfare. A contra-factual analysis of the consolidated results has shown that the Brazilian sugar standardization reduced the asymmetric information in this market. The impact of this policy was an increase in roughly 8 percent in the sugar production in 2006 due to the product standardization implemented in 1992. As a conclusion, the econometric analysis developed show that the standardization of products can be considered a powerful strategic tool. Not only to promote specific sector competitiveness, but also as an instrument to reduce the asymmetric information to the benefit of consumers.

The aim of this thesis is to apply and evaluate potential forecasting models for solar power production, based on data from a photovoltaic facility in Sala, Sweden. The thesis evaluates single step forecasting models as well as multiple step forecasting models, where the three compared models for single step forecasting are persistence, autoregressive integrated moving average (ARIMA) and ARIMAX. ARIMAX is an ARIMA model that also takes exogenous predictors in consideration. In this thesis the evaluated exogenous predictor is wind speed. The two compared multiple step models are multiple step persistence and the Gaussian process (GP). Root mean squared error (RMSE) is used as the measurement of evaluation and thus determining the accuracy of the models. Results show that the ARIMAX models performed most accurate in every simulation of the single step models implementation, which implies that adding the exogenous predictor wind speed increases the accuracy. However, the accuracy only increased by 0.04% at most, which is determined as a minimal amount. Moreover, the results show that the GP model was 3% more accurate than the multiple step persistence; however, the GP model could be further developed by adding more training data or exogenous variables to the model.

As aeronaves do tipo multirrotor têm sido crescentemente investigadas, particularmente o quadrirrotor. Estudos acerca dos VANTs (Veículos Aéreos Não Tripulados) apresentam o quadrirrotor como plataforma padrão, devido aos seus benefícios, tais como: baixo custo de construção, estabilidade de voo, percepção tridimensional e mobilidade, quando comparadas a outros tipos de aeronaves. Logo, caracteriza-se como um desafio na área de controle. Este fato faz com que haja a necessidade da aquisição do modelo matemático do conjunto de propulsão eletromecânico que compõe estas aeronaves. A fim de encontrar um modelo que melhor possa descrever os aspectos referentes ao sistema, utilizam-se de características específicas dos parâmetros do sistema, obtidas por meio de métodos de estimação de parâmetros, baseados nos mínimos quadrados e associados às técnicas de modelagem caixa preta. Nesse contexto, se propõem a obtenção do modelo matemático ARIMAX (AutoRegressive Integrated Moving Average Exogenous inputs) e ARMAX (AutoRegressive Moving Average with Exogenous inputs), a fim de comparar a performance entre os mesmos para cada estimador, utilizando como um dos critérios o menor número de iterações numéricas, pois caracteriza convergência rápida. A determinação dos parâmetros característicos dar-se-á por meio da utilização dos estimadores de Gauss-Newton e de Levenberg-Marquardt. A diretriz metodológica consiste na realização das etapas da Identificação de Sistemas. As simulações computacionais são realizadas no software MatLab, de acordo com a estrutura dos algoritmos de cada estimador proposto, e, as validações dos modelos e de seus parâmetros, se dão por comparação entre os dados do sistema real, obtidos a partir da planta didática (plataforma de testes), análises residuais e entre a performance dos modelos matemáticos. Constata-se que o modelo ARIMAX, através do método de Gauss-Newton, revela-se como o que melhor descreve o comportamento não linear do propulsor eletromecânico. O resultado desta investigação é uma contribuição à comunidade científica que busca modelar matematicamente os VANTs do tipo multirrotor. / 107 f.

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Accurate day-ahead grid loss forecasts are, among other things, essential to determine the electricity price for the upcoming day. The more accurate forecast, the closer the trading on the 'day-ahead' electricity market can become the actual operation the next day, which dedcrease the need for correcting production on the balancing market. Followingly, the need for extra imbalance costs, which make the electricity price higher, is reduced with accurate forecasts. This project's purpose was to explore a wide range of mathematical models to increase the energy comapny Fortum's day-ahead grid loss forecasting accuracy, and thereby contribute to lower the risk for high imbalance costs.  Two electrical grids located in Sweden, with different characteristics, were studied. One electrical grid was located in Dalarna and the other one was located in Värmland. Four different model types were tested for each grid. The linear models ARIMAX and SARIMAX were explored and the two artificial neural networks FNN (Feedforward Neural Network) and LSTM-RNN (Long-SHort Term Memory Recurrent Neural Network) were explored. By constructing different model structures of each model type, as well as statistically testing which predictors to include as input to the models, the most accurate model for grid loss forecasting was found. The models' forecasting accuracy were validated based on the MAPE (Mean Absolute Percentage Error). Variables important as predictors were found to be power production, electricity prices and grid losses at previous time steps. For the grid in Dalarna ARIMAX(2,0,2) was the model generating most accurate day-ahead grid loss forecasts and for the grid in Värmland, SARIMAX(1,0,0)(0,0,1)[24] was the most accurate model. That is, different models were found as the most accurate one for grid loss foracsting, as the two studied electricity grids had different characteristics. Hence, this result implies that there is no universal model that is the most adequate at modelling all types of grid losses. To find useful models when forecasting grid losses day-ahead, an analysis of the particular grid losses being studied is therefore not irrelevant.

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Improved sales forecasts for individual products in retail stores can have a positive effect both environmentally and economically. Historically these forecasts have been done through a combination of statistical measurements and experience. However, with the increased computational power available in modern computers, there has been an interest in applying machine learning for this problem. The aim of this thesis was to utilize two years of sales data, yearly calendar events, and weather data to investigate which machine learning method could forecast sales the best. The investigated methods were XGBoost, ARIMAX, LSTM, and Facebook Prophet. Overall the XGBoost and LSTM models performed the best and had a lower mean absolute value and symmetric mean percentage absolute error compared to the other models. However, Facebook Prophet performed the best in regards to root mean squared error and mean absolute error during the holiday season, indicating that Facebook Prophet was the best model for the holidays. The LSTM model could however quickly adapt during the holiday season improved the performance. Furthermore, the inclusion of weather did not improve the models significantly, and in some cases, the results were worsened. Thus, the results are inconclusive but indicate that the best model is dependent on the time period and goal of the forecast. / Förbättrade försäljningsprognoser för individuella produkter inom detaljhandeln kan leda till både en miljömässig och ekonomisk förbättring. Historiskt sett har dessa utförts genom en kombination av statistiska metoder och erfarenhet. Med den ökade beräkningskraften hos dagens datorer har intresset för att applicera maskininlärning på dessa problem ökat. Målet med detta examensarbete är därför att undersöka vilken maskininlärningsmetod som kunde prognostisera försäljning bäst. De undersökta metoderna var XGBoost, ARIMAX, LSTM och Facebook Prophet. Generellt presterade XGBoost och LSTM modellerna bäst då dem hade ett lägre mean absolute value och symmetric mean percentage absolute error jämfört med de andra modellerna. Dock, gällande root mean squared error hade Facebook Prophet bättre resultat under högtider, vilket indikerade att Facebook Prophet var den bäst lämpade modellen för att förutspå försäljningen under högtider. Dock, kunde LSTM modellen snabbt anpassa sig och förbättrade estimeringarna. Inkluderingen av väderdata i modellerna resulterade inte i några markanta förbättringar och gav i vissa fall även försämringar. Övergripande, var resultaten tvetydiga men indikerar att den bästa modellen är beroende av prognosens tidsperiod och mål.