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The purpose of this thesis is to test whether the probability of falsely rejecting a true null hypothesis of a model intercept being equal to zero is consistent with the chosen significance level when modelling the variance of the error term using GARCH (1,1), TGARCH (1,1) or IGARCH (1,1) models. We test this by estimating “Jensen’s alpha” to evaluate alpha trading, using a Monte Carlo simulation based on historical data from the Standard & Poor’s 500 Index and stocks in the Dow Jones Industrial Average Index. We evaluate over simulated daily data ranging over periods of 3 months, 6 months, and 1 year. Our results indicate that the GARCH and IGARCH consistently reject a true null hypothesis less often than the selected 1%, 5%, or 10%, whereas the TGARCH consistently rejects a true null more often than the chosen significance level. Thus, there is a risk of incorrect inferences when using these GARCH-type models.

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Den här uppsatsen inleds med att studera de moment som används för multinomial logistisk regression och hur resultaten mäts. Teorin tar sin avsats i den binomiala logistiska regression, för att stegvis ta sig vidare till den multinomiala logistiska regressionen. Begreppen logit, oddskvoten och sannolikheterna förtydligas, effekterna av de oberoende variablerna diskuteras och kopplingen till vanlig linjär regression åskådliggörs. Det blir även en fördjupning av matematiken bakom den logistiska funktionen. Därefter tillämpas den multinomial logistisk regressionsanalysen med ett praktiskt exempel. Analysmodellen är användbar inom flertalet områden och den här uppsatsen ligger inom ramen för sportanalys. Matchstatistik från ishockey och närmare bestämt Örebro Hockeys matcher från säsongerna 2012/13 till 2017/18 nyttjas och den slutgiltiga modellen använder sig av tre förklarande variabler. Resultatet visar att utfallet efter ordinarie tid kan förklaras till 60,9% med hjälp av matchstatistiken, vilket tyder på att den multinomiala regressionsmodellen presterar likvärdigt med andra metoder som tillämpar kategorisk dataanalys inom sportanalys. / This thesis starts by studying the multinomial logistic regression and its moments and how the results are measured. The theory begins with the binomial logistics regression and gradually moves on towards the multinomial logistics regression. Concepts as logit, odds ratio and probabilities are explained, the effects of the independent variables discussed and the link to ordinary linear regression is illustrated. There will also be a deeper, mathematical look at the function of logistic growth. Thereafter the multinomial logistic regression model will be applied. The model is useful within several domains and this thesis lies within sportsanalytics. For this thesis matchstatistics from ice hockey, that is Örebro Hockey’s matches from season 2012/13 to 2017/18, has been used and the final model has three exploratory variables. The outcome of the result performs equivalent to other methods, which applies categorical data analysis within sportsanalytics.

Financial markets have been crucial in driving capital investments across the world. Anessential piece of these markets is the presence of risk takers, or market speculators, who will hold financial portfolios in hopes of profit. Portfolios with cash flowsgenerated from floating interest rate derivatives will often be subjected to fixing risk, also called second-order basis risk, stemming from a discrepancy in time with the hedge and the original position. Using data from a fixing risk mitigation service, named RESET, this thesis aims todeepen the understanding of accumulation of fixing risk on the the USD dollar market for 3-month interest rate swaps. This is done by modeling customer behavior using machine learning methods. Macroeconomic factors such as market volatility and the January effect amongst others were incorporated as variables into the set. The two models explored are logistic regression and neural networks, the first one chosen for interoperability and the latter for its generality. Neither of the two models could accurately predict customer behavior, with a balanced accuracy short of 70 percent. The strongest influence of the final prediction turned out to be previous behavior, the January effect and how many of their financial positions the customer previously put into the service.

Previous research suggests that a specific biomarker measured in the blood correlates with cancer status, for a specific type of cancer: higher values of the biomarker are generally found in patients with progressive cancer. The aim of this study is to investigate this relationship using a Linear mixed model. Patients with a progressive disease have on average significantly higher values of the log of the biomarker and patients with partial or complete remission of the disease have on average significantly lower values of the logged biomarker, both compared to patients with a stable disease. Also, patients with a liver tumor have on average higher values of the log of the biomarker, compared to patients without. Including both a random intercept and a random slope in the Linear mixed model, in addition to the fixed effects, results in the best model fit. Due to the non-random sample used, these results are only valid for this specific sample but can be of guidance for the conduction and planning of future studies.