This master thesis is focused on analysis and forecasting of hourly and daily electricity price on the deregulated Czech daily electricity market. The methods used for estimating and forecasting hourly and daily prices are picked from the ARIMA-GARCH family of models and Neural Networks. For daily price data, the Redundant Haar Wavelet Transform decomposition of the time series is used in combination with ARIMA and Neural Networks models for forecasting. For hourly data, ARIMA and Neural Network models are considered. The forecasting results of daily data indicate that simpler models such as seasonal ARIMA outperform all other methods. Also the wavelet decomposi- tion of the daily series didn't prove useful in enhancing the forecast precision. For hourly data, the Multilayer Perceptron architecture of the neural network outperformed the ARIMA forecast. JEL Classification C20, C22, C45, C53, C65 Keywords Forecasting, Time Series, ARIMA, GARCH, Neural Net- works, Wavelet Transform Author's e-mail krystof.cerny@gmail.com Supervisor's e-mail lebovicm@gmail.com 1

n the electrical power grid, the power load is not constant but continuouslychanging. This depends on many different factors, among which the habits of theconsumers, the yearly seasons and the hour of the day. The continuous change inenergy consumption requires the power grid to be flexible. If the energy provided bygenerators is lower than the demand, this is usually compensated by using renewablepower sources or stored energy until the power generators have adapted to the newdemand. However, if buffers are depleted the output may not meet the demandedpower and could cause power outages. The currently adopted practice in the indus-try is based on configuring the grid depending on some expected power draw. Thisanalysis is usually performed at a high level and provide only some basic load aggre-gate as an output. In this thesis, we aim at investigating techniques that are able topredict the behaviour of loads with fine-grained precision. These techniques couldbe used as predictors to dynamically adapt the grid at run time. We have investigatedthe field of time series forecasting and evaluated and compared different techniquesusing a real data set of the load of the Swedish power grid recorded hourly throughyears. In particular, we have compared the traditional ARIMA models to a neuralnetwork and a long short-term memory (LSTM) model to see which of these tech-niques had the lowest forecasting error in our scenario. Our results show that theLSTM model outperformed the other tested models with an average error of 6,1%.

Antibiotic resistant bacteria, a growing health crisis, arise due to antibiotic overuse and misuse. Resistant infections endanger the lives of patients and are financially burdensome. Aggregate antimicrobial susceptibility reports, called antibiograms, are critical for tracking antibiotic susceptibility and evaluating the likelihood of the effectiveness of different antibiotics to treat an infection prior to the availability of patient specific susceptibility data. This research leverages the Massachusetts Statewide Antibiogram database, a rich dataset composed of antibiograms for $754$ antibiotic-bacteria pairs collected by the Massachusetts Department of Public Health from $2002$ to $2016$. However, these antibiograms are at least a year old, meaning antibiotics are prescribed based on outdated data which unnecessarily furthers resistance. Our objective is to employ data science techniques on these antibiograms to assist in developing more responsible antibiotic prescription practices. First, we use model selectors with regression-based techniques to forecast the current antimicrobial resistance. Next, we develop an assistant to immediately identify clinically and statistically significant changes in antimicrobial resistance between years once the most recent year of antibiograms are collected. Lastly, we use k-means clustering on resistance trends to detect antibiotic-bacteria pairs with resistance trends for which forecasting will not be effective. These three strategies can be implemented to guide more responsible antibiotic prescription practices and thus reduce unnecessary increases in antibiotic resistance.

Antibiotic resistant bacteria, a growing health crisis, arise due to antibiotic overuse and misuse. Resistant infections endanger the lives of patients and are financially burdensome. Aggregate antimicrobial susceptibility reports, called antibiograms, are critical for tracking antibiotic susceptibility and evaluating the likelihood of the effectiveness of different antibiotics to treat an infection prior to the availability of patient specific susceptibility data. This research leverages the Massachusetts Statewide Antibiogram database, a rich dataset composed of antibiograms for $754$ antibiotic-bacteria pairs collected by the Massachusetts Department of Public Health from $2002$ to $2016$. However, these antibiograms are at least a year old, meaning antibiotics are prescribed based on outdated data which unnecessarily furthers resistance. Our objective is to employ data science techniques on these antibiograms to assist in developing more responsible antibiotic prescription practices. First, we use model selectors with regression-based techniques to forecast the current antimicrobial resistance. Next, we develop an assistant to immediately identify clinically and statistically significant changes in antimicrobial resistance between years once the most recent year of antibiograms are collected. Lastly, we use k-means clustering on resistance trends to detect antibiotic-bacteria pairs with resistance trends for which forecasting will not be effective. These three strategies can be implemented to guide more responsible antibiotic prescription practices and thus reduce unnecessary increases in antibiotic resistance.

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.

Os processos espaço-temporais vêm ganhando destaque nos últimos anos, em razão do aumento de estudos compreendendo variáveis que apresentam interação entre as dimensões espacial e temporal. Com o objetivo de modelar esses processos, Pfeifer e Deutsch (1980a) propuseram uma extensão da classe de modelos univariados de Box-Jenkins, denominada por modelo espaço-temporal autoregressivo de média móvel (STARMA). Essa classe de modelos é utilizada para descrever dados de séries temporais espacialmente localizadas. Os processos passíveis de modelagem via classe de modelos STARMA são caracterizados por observações de variáveis aleatórias, em que os locais a serem incorporados no modelo são fixos no espaço. A dependência entre as n séries temporais é modelada por meio da matriz de ponderação, de modo que os modelos da classe STARMA expressem cada observação no tempo t e na localização i como uma média ponderada de combinações lineares das observações anteriores e a inovação defasada no espaço e no tempo conjuntamente. Dada a nova classe de modelos, os objetivos deste estudo foram apresentar a classe de modelos STARMA, implentar computacionalmente, no software R, rotinas que permitam a análise de dados espaço-temporais, com as rotinas implementadas estabelecer e testar modelos de séries temporais aos dados de temperaturas mínimas médias mensais de 8 estações meteorológicas situadas no Paraná e comparar a classe de modelos STARMA com a classe de modelos univariados proposta por Box e Jenkins (1970). Com este estudo verificou-se que na apresentação da classe de modelos STARMA há complexidade no conceito de ordens de vizinhança e na identificação dos modelos espaço-temporais. Em relação a criação de rotinas responsáveis pelas análises de dados espaço-temporais observou-se dificuldades em sua implementação, principalmente no momento de estimação dos parâmetros. Na comparação da classe de modelos STARMA, multivariada, com a classe de modelos SARIMA, univariada, constatou-se que ambos os modelos se ajustaram de maneira satisfatória aos dados, produzindo previsões acuradas. / Spatio-temporal processes have been highlighted lately, due to the increase of studies approaching variables that present interactions between the spatial and temporal dimensions. In order to model these processes, Pfeifer e Deutsch (1980a) have suggested an extension of the Box-Jenkins univariate model class, named spatio-temporal autoregressive moving-average model (STARMA). This model class is used to describe spatially located time series data. The processes prone to be modeled via the STARMA model class are characterized by observations of random variables, in which the locations to be incorporated in the model are spatially fixed. The dependence between the n time series is modeled through the weighing matrix. So STARMA models express each observation at time t and location i as a weighed mean of linear combinations of the previous observations and the jointly lagged innovation in space and time. Given the new class models, the objectives of this study were to present a class of models STARMA, implentar computationally, in textit R software, routines that allow the analysis of spatio-temporal data with the routines implemented to establish and test models time series data of monthly average minimum temperatures of 8 meteorological stations located in Paraná and compare the class of models STARMA with the class of univariate models proposed by Box e Jenkins (1970). With this study it was found that the presentation of the class of models STARMA no complexity in the concept of ordered neighborhood and identification of spatio-temporal models. Regarding the creation of routines responsible for the analysis of spatio-temporal observed difficulties in its implementation, especially at the time of estimation of parameters. In comparison class STARMA models, multivariate, with the class of SARIMA models, univariate, it was found that both models were adjusted satisfactorily to the data, producing accurate forecasts.

In this thesis, player’s performance on ice hockey is modelled to create newmetricsby match and season for players. AD-trees have been used to summarize ice hockey matches using state variables, which combine context and action variables to estimate the impact of each action under that specific state using Markov Decision Processes. With that, an impact measure has been described and four player metrics have been derived by match for regular seasons 2007-2008 and 2008-2009. General analysis has been performed for these metrics and ARIMA models have been used to analyze and predict players performance. The best prediction achieved in the modelling is the mean of the previous matches. The combination of several metrics including the ones created in this thesis could be combined to evaluate player’s performance using salary ranges to indicate whether a player is worth hiring/maintaining/firing

The purpose of this report is to predict annual insurance data with quarterly data as predictors and to evaluate its accuracy against other naive prediction models. A relationship is discerned between the two data categories and the interest goes beyond publication frequency as there is a fundamental difference between quarterly and annual data. The insurance industry organization Insurance Sweden publishes quarterly data that contain all insurance events reported while the annual data only contain insurance events which led to disbursement from the insurance companies. This discrepancy shows to be problematic when predicting annual outcomes. Forecasts are estimated by ARIMA models on short time series and compared with classic linear regression models. The implied results from all insurance subcategories in traffic, motor vehicles and household- and corporate insurance are that, in some cases, prediction using linear regression on quarterly data is more precise than the constructed naive prediction models on annual data. However, the results vary between subcategories and the regression models using quarterly data need further improvement before it is the obvious choice when forecasting annual number of events that led to disbursements from the insurance companies.

2009年至2011年，倫敦金屬交易所(LME)銅價出現大幅上升行情，LME銅價自3,260美元/噸，於2011年一月達到9,532美元/噸，漲幅92%，銅價逐漸上揚，隨著世界經濟的復甦，全球銅市場再度擁有上揚的推力，創下歷史的新高，且有挑戰更高價格的趨勢。 目前銅箔基層板為印刷電路板之基礎材料，被廣泛運用在民生家電、電腦、通訊、醫療、軍事用途。而所需要使用的銅原料都必須仰賴進口，因而企業在面臨強大的競爭壓力下，要如何避免銅價的波動所帶來的威脅，就成為企業重要的課題之一。目前國內尚未有對於銅價避險之研究，本研究將透過避險策略，以提供給企業對於銅原料成本管理擬定避險策略之參考。 本研究以LME銅價以及上海期貨交易所(SHEF)銅價作為資料分析的基礎。利用ARIMA模型判斷LME及SHEF銅價最適合之模型，研究結果顯示LME銅價為ARIMA(4,1,4)，SHEF銅價為(2,1,2)，在以LME銅價預測模型及避險策略判斷何時適用哪種避險方法，實證結果顯示： 1. 若預測未來趨勢為盤整階段，適用Collar、Leveraged TARN Swap、Leveraged Range Swap及Leveraged Knockout Forward。 2. 若預測未來趨勢為小跌，適用Fixed Swap、Extendible Fixed Swap、Leveraged TARN Swap、Leveraged Range Swap及Leveraged Knockout Forward。 3. 若預測未來趨勢為大跌，適用Fixed Swap及Extendible Fixed Swap。

<p>With the development of the financial markets, the foreign exchange market has become more and more important for investors. The daily volume of business dealt with on the foreign exchange markets in 1998 was estimated to be over $2.5 trillion dollars (the daily volume on New York Stock Exchanges is about $20 billion). Today (2006) it may be about $5 trillion dollars. More and more people notice the foreign exchange market, and more and more sophisticated investors research such markets. The purpose of this thesis is to compare different methods to forecast the exchange rate of the money pair AUD/JPY. Firstly we studied the relationship between the AUD/JPY exchange rate and some economic fundamentals by using a regression model. Secondly, we tested whether the AUD/JPY exchange rate had any relationship with its historical records by using an ARIMA model. Finally, we compared the two model forecasting performance. A secondary purpose is to test whether the Market Efficiency Hypothesis works on the money pair AUD/JPY. In the study, data from January 1986 to June 2006 were chosen. To test which method produces better forecasts, we chose data from January 1986 to December 2002 to build up the prediction functions. Then we used the data from January 2003 to 2006 June to evaluate which predicting method was closer to the reality. In the comparison of the forecasting performances, two approaches dealing with the unknown future fundamentals were used. Firstly we assumed that we could do perfect predictions of these regressors, that was, our predictions of these regressors were the same as the actual future outcomes. So we put the real data for the fundamentals from January 2003 to June 2006 into the regression function. Secondly we assumed that we were in real life situation, and we had to predict the regressors first in order to get the predictions of the exchange rate. The results of the comparison were that the AUD/JPY exchange rate could to some extent be predictable, and that the predictions by the ARIMA model were more accurate.</p>