This thesis is focused on mathematical modelling of exchange rate CZK/USD in 1991 - 2014. Time series was divided into 5 parts. First Box-Jenkins methodology models were examined, especially ARIMA model. Unfortunately, the model could not be used because none of the time series showed correlation. The time series is considered as a white noise. The data appear to be completely random and unpredictable. The time series have not constant variance neither normal distribution and therefore GARCH volatility model was used as the second model. It is better not to divide time series when using model of volatility. Volatility model contributes to more accurate prediction than the standard deviation. Results were calculated in RStudio software and MS Excel.

This thesis analyzes the monthly data from historical series of the heat stroke cycles, solar radiation and average wind speeds in the 1961 and 2008 period to identify long-term inaccuracies in the location of both wind and solar sources. The state of Rio Grande do Sul-Brazil, was chosen as a case study, to estimate the behavioral trend of these variables and compare them with the measured data, testing the homogeneity of information. Therefore, it aims at improving the long-term prognosis in locating projects of solar power generation plants. The analysis of these climatic variables was carried out using ARIMA models (autoregressive integrated moving average models) as well as the Box & Jenkins methodology and seasonality studies with the X11 ARIMA models with 5% statistical significance. In this study, the period between 1961 and 2011 indicated that heat stroke rates were not enough to overcome the values recorded in the 1960s and 1970s, when the percentages were in most months 1% below the historical average. The observed heat stroke data suggest decreasing trends in the 1980s and 1990s, due to the presence of the phenomenon called "global dimming", which contributed to lower levels of solar radiation.!A possible structural break has been found in the wind series from August 2001 through the CUSUMQ test (cumulative sum of squares of recursive waste) and the Lane et al test. (2002), leading to higher values and overestimating the final prognosis of wind power. A decrease in the average wind speed was also observed from 2003 to 2011 during six months of these years.!The spring season, often with the highest wind potential had the highest mean decrease while the season with the lowest wind potential, fall, had the opposite behavior during the studied period. By spectral analysis, performed by Fourier method, the time series of sunshine and solar radiation also showed cycles with possible ranges of influence on measurements of the solar energy potential. Such temporal variations in the data, indicate that possible locations for the wind and photovoltaic plants may be seriously affected since longterm weather fluctuations can vary significantly even at the best location selected to generate electricity. / Esta tese analisa os dados mensais das séries históricas dos ciclos de insolação, radiação solar e velocidade média dos ventos para melhorar o prognóstico de longo prazo na localização de áreas para fontes eólicas e solares de geração de potência elétrica. Como estudo de caso, tomou-se o período de dados de 1961 a 2008 para definir imprecisões de longo prazo que podem ocorrer no estado do Rio Grande do Sul, Brasil, na estimativa da tendência comportamental das variáveis meteorológicas e compará-las com dados medidos, testando assim, a homogeneidade das informações. As análises das variáveis climáticas foram realizadas através de modelos ARIMA (modelos autorregressivos integrados de média móvel), por meio da metodologia Box & Jenkins e do estudo da sazonalidade com modelos X11 ARIMA em níveis de significância estatística de 5%. Neste estudo, o período entre 1961 e 2011 indicou que os índices de insolação não foram suficientes para superar os valores verificados nas décadas de 1960 e 1970, em que os percentuais foram na maioria dos meses da ordem de -1% abaixo da média histórica. Os dados observados da insolação sugerem tendências decrescentes nas décadas de 1980 e 1990, pela presença do fenômeno global dimming sobre o estado do Rio Grande do Sul contribuindo para menores níveis de radiação solar. Foi constatada também uma possível quebra estrutural na série eólica em agosto de 2001 através do teste CUSUMQ (soma acumulada dos quadrados dos resíduos recursivos) e do teste de Lane et al. (2002), conduzindo a valores maiores e superestimando o prognóstico final do potencial eólico. Também foi constatada, redução em seis dos doze meses do ano na velocidade média dos ventos no período de 2003 a 2011. A estação da primavera, geralmente com o maior potencial eólico, indicou uma maior média de redução enquanto a estação de menor potencial eólico, o outono, mostrou um comportamento inverso para este mesmo período. Através da análise espectral, realizada pelo método de Fourier, as séries históricas de insolação e radiação solar mostraram também ciclos com amplitudes possíveis de influenciar as mensurações do potencial energético solar. Com estas variações temporais nos dados, as previsões de localização de centrais eólicas e fotovoltaicas ficam seriamente prejudicadas, uma vez que as oscilações meteorológicas de longo prazo podem variar sensivelmente na melhor localização de áreas para geração de energia elétrica.

Valutamarknaden är världens största marknad och en nödvändig del av dagens globala samhälle, som gör det möjligt för företag att göra affärer i olika valutor och mellan olika gränser. Marknaden utgör en stor handelsplattform för både små och stora aktörer, för vilka det är viktigt att prognostisera valutakurser med gott resultat. Att modellera finansiella instrument i form av tidsserier är en av de vanligaste investeringsstrategierna och dess användningsområde sträcker sig från valutamarknaden till bland annat aktiemarknaden och råvarumarknaden. I denna uppsats undersöks fyra olika statistiska metoder för att modellera valutakursen Euro-US Dollar givet historisk data, och prognoser görs med de framtagna modellerna. Dessa metoder är slumpvandring, ARIMA, ARIMA-GARCH och VAR. Vidare undersöks för den dynamiska VAR-modellen hur valutamarkanden påverkar, och blir påverkad av, långa och korta räntan. Resultaten visar att ARIMA(3,1,2) förklarar valutakursen bäst medan VAR(2) med valutakursen och skillnaden mellan långa räntor som ingående variabler ger de bästa prediktionerna. / The foreign exchange market is the world’s largest market and is an essential part of the global society of today. The FX market enables companies to trade with different currencies across country borders. It is also a large trade-platform for both big and small financial actors, who greatly benefit from the advantages of good predictions. Modeling of financial instruments is one of the most commonly used investment strategies and its area of application ranges from the FX market to markets suchas the stock market and the commodity market. In this paper, four different statistical models are used to model the currency pair Euro-US Dollar. These methods are random walk, ARIMA, ARIMA-GARCH and VAR. Besides investigating which method that gives the best forecasts, the method that best describes the training datais also found. Furthermore, for the dynamic VAR model, it is explored how the FX market affects, and is affected by, the long term and short term interest. The results show that ARIMA(3,1,2) is the best at describing the exchange rate while VAR(2) with the exchange rate and the difference between long term interests as variables gives the best predictions.

[pt] Nesta dissertação é desenvolvida uma metodologia para previsão de demanda mensal de energia elétrica considerando cenários de racionamento. A metodologia usada consiste em, a partir das taxas de crescimento da série temporal, identificar e eliminar os efeitos do racionamento de energia elétrica através da aplicação de Modelos Lineares Dinâmicos. São analisadas também estruturas de intervenção nos modelos estatísticos de Box & Jenkins e Holt & Winters. Os modelos são então comparados segundo alguns critérios, basicamente no que tange à sua eficiência preditiva. Conclui-se ao final sobre a eficiência da metodologia proposta, dado a grande dificuldade para solucionar o problema a partir dos modelos estatísticos de Box & Jenkins e Holt & Winters. Esta solução é então proposta como a mais viável para criar cenários de racionamento e pósracionamento de energia para ser utilizado por agentes do sistema elétrico nacional. / [en] In this dissertation, a methodology is developed to forecast monthly demand of electric energy, considering the rationing scenery. The methodology is based on, taking the growth rate from the time series, identify and eliminate the effects of electric energy rationing, using Dynamic Linear Models. It is also analyzed intervention structures in the statistics models of Box & Jenkins and Holt & Winters. The models are compared according to some criterions, mainly forecast accuracy. At the end, we concluded that the methodology proposed is more efficient, due to the difficult to solve the problem using the statistics models with intervention. This solution is proposed as the best among them to create scenery during the energy rationing and after energy rationing, to be used by the national electric system agents.

Deep learning techniques have exhibited remarkable capabilities in capturing nonlinear patterns and dependencies in time series data. Therefore, this study investigates the application of the Long-Short-Term-Memory (LSTM) algorithm for stock price prediction in intraday quantitative trading using Swedish stocks in the OMXS30 index from February 28, 2013, to March 1, 2023. Contrary to previous research [12, 32] suggesting that past movements or trends in stock prices cannot predict future movements, our analysis finds limited evidence supporting this claim during periods of high volatility. We discover that incorporating stock-specific technical indicators does not significantly enhance the predictive capacity of the model. Instead, we observe a trade-off: by removing the seasonal component and leveraging feature engineering and hyperparameter tuning, the LSTM model becomes proficient at predicting stock price movements. Consequently, the model consistently demonstrates high accuracy in determining price direction due to consistent seasonality. Additionally, training the model on predicted return differences, rather than the magnitude of prices, further improves accuracy. By incorporating a novel long-only and long-short trading strategy using the one-day-ahead predictive price, our model effectively captures stock price movements and exploits market inefficiencies, ultimately maximizing portfolio returns. Consistent with prior research [14, 15, 31, 32], our LSTM model outperforms the ARIMA model in accurately predicting one-day-ahead stock prices. Portfolio returns consistently outperforms the stock market index, generating profits over the entire time period. The optimal portfolio achieves an average daily return of 1.2%, surpassing the 0.1% average daily return of the OMXS30 Index. The algorithmic trading model demonstrates exceptional precision with a 0.996 accuracy rate in executing trades, leveraging predicted directional stock movements. The algorithmic trading model demonstrates an impressive 0.996 accuracy when executing trades based on predicted directional stock movements. This remarkable performance leads to cumulative and annualized excessive returns that surpass the index return for the same period by a staggering factor of 800. / Djupinlärningstekniker har visat en enastående förmåga att fånga icke-linjära mönster och samband i tidsseriedata. Med detta som utgångspunkt undersöker denna studie användningen av Long-Short-Term-Memory (LSTM)-algoritmen för att förutsäga aktiepriser med svenska aktier i OMXS30-indexet från den 28 februari 2013 till den 1 mars 2023. Vår analys finner begränsat stöd till tidigare forskning [12, 32] som hävdar att historisk aktierörelse eller trend inte kan användas för att prognostisera framtida mönster. Genom att inkludera aktiespecifika tekniska indikatorer observerar vi ingen betydande förbättring i modellens prognosförmåga. genom att extrahera den periodiska komponenten och tillämpa metoder för egenskapskonstruktion och optimering av hyperparametrar, lär sig LSTM-modellen användbara egenskaper och blir därmed skicklig på att förutsäga akrieprisrörelser. Modellen visar konsekvent högre noggrannhet när det gäller att bestämma prisriktning på grund av den regelbundna säsongsvariationen. Genom att träna modellen att förutse avkastningsskillnader istället för absoluta prisvärden, förbättras noggrannheten avsevärt. Resultat tillämpas sedan på intradagshandel, där förutsagda stängningspriser för nästkommande dag integreras med både en lång och en lång-kort strategi. Vår modell lyckas effektivt fånga aktieprisrörelser och dra nytta av ineffektiviteter på marknaden, vilket resulterar i maximal portföljavkastning. LSTM-modellen är överlägset bättre än ARIMA-modellen när det gäller att korrekt förutsäga aktiepriser för nästkommande dag, i linje med tidigare forskning [14, 15, 31, 32], är . Resultat från intradagshandeln visar att LSTM-modellen konsekvent genererar en bättre portföljavkastning jämfört med både ARIMA-modellen och dess jämförelseindex. Dessutom uppnår strategin positiv avkastning under hela den analyserade tidsperioden. Den optimala portföljen uppnår en genomsnittlig daglig avkastning på 1.2%, vilket överstiger OMXS30-indexets genomsnittliga dagliga avkastning på 0.1%. Handelsalgoritmen är oerhört exakt med en korrekthetsnivå på 0.996 när den genomför affärer baserat på förutsagda rörelser i aktiepriset. Detta resulterar i en imponerande avkastning som växer exponentiellt och överträffar jämförelseindex med en faktor på 800 under samma period.

Temperature regulation in buildings can be tricky and expensive. A common problem when heating buildings is that an unnecessary amount of energy is supplied. This waste of energy is often caused by a faulty regulation system. This thesis presents a machine learning ap- proach, using time series data, to predict the energy supply needed to keep the inside tem- perature at around 21 degrees Celsius. The machine learning models LSTM, Ensemble LSTM, AT-LSTM, ARIMA, and XGBoost were used for this project. The validation showed that the ensemble LSTM model gave the most accurate predictions with the Mean Absolute Error of 22486.79 (Wh) and Symmetric Mean Absolute Percentage Error of 5.41 % and was the model used for comparison with the current system. From the performance of the different models, the conclusion is that machine learning can be a useful tool to pre- dict the energy supply. But on the other hand, there exist other complex factors that need to be given more attention to, to evaluate the model in a better way. / Temperaturreglering i byggnader kan vara knepigt och dyrt. Ett vanligt problem vid upp- värmning av byggnader är att det tillförs onödigt mycket energi. Detta energispill orsakas oftast av ett felaktigt regleringssystem. Denna rapport studerar möjligheten att, med hjälp av tidsseriedata, kunna träna olika maskininlärningmodeller för att förutsäga den energitill- försel som behövs för att hålla inomhustemperaturen runt 21 grader Celsius. Maskininlär- ningsmodellerna LSTM, Ensemble LSTM, AT-LSTM, ARIMA och XGBoost användes för detta projekt. Valideringen visade att ensemble LSTM-modellen gav den mest exakta förut- sägelserna med Mean Absolute Error på 22486.79 (Wh) och Symmetric Mean Absolute Percentage Error på 5.41% och var modellen som användes för att jämföra med det befint- liga systemet. Från modellernas prestation är slutsatsen att maskininlärning kan vara ett an- vändbart verktyg för att förutsäga energitillförseln. Men å andra sidan finns det andra kom- plexa faktorer som bör tas hänsyn till så att modellen kan evalueras på ett bättre sätt.

Financial institutions manage numerous portfolios whose risk must be managed continuously, and the large amounts of data that has to be processed renders this a considerable effort. As such, a system that autonomously detects anomalies in the risk measures of financial portfolios, would be of great value. To this end, the two econometric models ARMA-GARCH and EWMA, and the two machine learning based algorithms LSTM and HTM, were evaluated for the task of performing unsupervised anomaly detection on the streaming time series of portfolio risk measures. Three datasets of returns and Value-at-Risk series were synthesized and one dataset of real-world Value-at-Risk series had labels handcrafted for the experiments in this thesis. The results revealed that the LSTM has great potential in this domain, due to an ability to adapt to different types of time series and for being effective at finding a wide range of anomalies. However, the EWMA had the benefit of being faster and more interpretable, but lacked the ability to capture anomalous trends. The ARMA-GARCH was found to have difficulties in finding a good fit to the time series of risk measures, resulting in poor performance, and the HTM was outperformed by the other algorithms in every regard, due to an inability to learn the autoregressive behaviour of the time series. / Finansiella institutioner hanterar otaliga portföljer vars risk måste hanteras kontinuerligt, och den stora mängden data som måste processeras gör detta till ett omfattande uppgift. Därför skulle ett system som autonomt kan upptäcka avvikelser i de finansiella portföljernas riskmått, vara av stort värde. I detta syftet undersöks två ekonometriska modeller, ARMA-GARCH och EWMA, samt två maskininlärningsmodeller, LSTM och HTM, för ändamålet att kunna utföra så kallad oövervakad avvikelsedetektering på den strömande tidsseriedata av portföljriskmått. Tre dataset syntetiserades med avkastningar och Value-at-Risk serier, och ett dataset med verkliga Value-at-Risk serier fick handgjorda etiketter till experimenten i denna avhandling. Resultaten visade att LSTM har stor potential i denna domänen, tack vare sin förmåga att anpassa sig till olika typer av tidsserier och för att effektivt lyckas finna varierade sorters anomalier. Däremot så hade EWMA fördelen av att vara den snabbaste och enklaste att tolka, men den saknade förmågan att finna avvikande trender. ARMA-GARCH hade svårigheter med att modellera tidsserier utav riskmått, vilket resulterade i att den preseterade dåligt. HTM blev utpresterad utav de andra algoritmerna i samtliga hänseenden, på grund utav dess oförmåga att lära sig tidsserierna autoregressiva beteende.

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.

[pt] Tendo em vista mudanças significativas no varejo causadas pelo crescimento de compras online no Brasil, este estudo tem como objetivo facilitar um relevante lead time e um forte grau de assertividade na previsão de demanda do Omnichannel de uma empresa do setor. Com a crescente relevância do Omnichannel, é importante compreender as necessidades dos consumidores tradicionais e digitais, integrar suas experiências e oferecer múltiplos canais de compra. Nesse contexto, a previsão de demanda é crucial para apoiar as decisões estratégicas, táticas e operacionais da organização. A utilização de séries temporais hierárquicas auxilia na precisão das previsões e, portanto, na tomada de decisões, permitindo gerar estimativas coerentes ao longo dos múltiplos níveis hierárquicos. Dessa forma, neste estudo, combinando as metodologias de previsão de séries temporais ETS, ARIMA e SARIMAX, com métodos de reconciliação Bottom-up, Top-down, MinTrace Combinação Ótima (OLS) e MinTrace WLS Struct, doze modelos foram gerados. Baseado nas principais abordagens de séries temporais hierárquicas, com uma sequência de sete passos, os modelos foram comparados, por meio de métricas de avaliação de desempenho, para identificar qual deles melhor se encaixa na série trabalhada. Ao final do estudo, o modelo SARIMAX com Bottom-up se mostrou a combinação mais adequada para a série em análise. A abordagem alcançou um MAPE de 22 por cento no nível mais agregado da hierarquia, reduzindo em cinco pontos percentuais o MAPE original da empresa, além de apresentar a melhor colocação na combinação das métricas comparativamente. / [en] In light of recent changes in retail caused by the growth of online shopping in Brazil, this study aims to enable a substantial lead time and a high degree of accuracy of the Omnichannel demand forecast for a retail company. As Omnichannel success continues to expand, it becomes increasingly important tounderstand the needs of both traditional and digital consumers, integrate their experiences and offer multiple purchase channels. In this context, demand forecasting is crucial for identifying market trends, growth opportunities, potentialstrategies and supporting strategic, tactical and operational decisions. The use of Hierarchical Time Series improves forecasts accuracy and, therefore, assists in decision-making, allowing the development of consistent estimations acrossmultiple hierarchical levels. Thus, this study combines the time series forecast generation methodologies ETS, ARIMA and SARIMAX, with Bottom-up, Top-down, MinTrace Optimal Combination (OLS) and MinTrace WLS Struct reconciliation methods, resulting in the generation of twelve models. Based on the main theories of Hierarchical Time Series and following a 7-steps sequence, the models were compared using performance evaluation metrics to identify the best fit for the investigated series. The research concludes that the SARIMAX model,together with the Bottom-up strategy, proves to be the most appropriate composition for the Hierarchical Time Series under analysis, as it demonstrates the best performance across the evaluation metrics, reaching a MAPE of 22 percent at the most aggregated level of the hierarchy and reducing the original company forecasting MAPE by five percentage points.

Econometric and predictive modeling techniques are two popular forecasting techniques. Both ofthese techniques have their own advantages and disadvantages. In this thesis some econometricmodels are considered and compared to predictive models using sales data for five products fromICA a Swedish retail wholesaler. The econometric models considered are regression model,exponential smoothing, and ARIMA model. The predictive models considered are artificialneural network (ANN) and ensemble of neural networks. Evaluation metrics used for thecomparison are: MAPE, WMAPE, MAE, RMSE, and linear correlation. The result of this thesisshows that artificial neural network is more accurate in forecasting sales of product. But it doesnot differ too much from linear regression in terms of accuracy. Therefore the linear regressionmodel which has the advantage of being comprehensible can be used as an alternative to artificialneural network. The results also show that the use of several metrics contribute in evaluatingmodels for forecasting sales. / Program: Magisterutbildning i informatik