In this thesis, a Bayesian approach is adopted to handle parameter estimation and model uncertainty in autoregressive moving average (ARMA) time series models and dynamic linear models (DLM). Bayesian model uncertainty is handled in a parametric fashion through the use of posterior model probabilities computed via Markov chain Monte Carlo (MCMC) simulation techniques. Attention is focused on reversible jump Markov chain Monte Carlo (RJMCMC) samplers, which can move between models of different dimensions, to address the problem of model order uncertainty and strategies for proposing efficient sampling schemes in autoregressive moving average time series models and dynamic linear models are developed. The general problem of assessing convergence of the sampler in a dimension-changing context is addressed by computing estimates of the probabilities of moving to higher and lower dimensional spaces. Graphical and numerical techniques are used to compare different updating schemes. The methodology is illustrated by applying it to both simulated and real data sets and the results for the Bayesian model selection and parameter estimation procedures are compared with the classical model selection criteria and maximum likelihood estimation.

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Vertical alliances are an increasingly common form of organization for participants in the beef industry. The implications of combining feeding and packing margins into one alliance are investigated. Moving average based selective hedging strategies are used to hedge the major inputs and outputs for cattle owners and packers to improve the level of mean revenue to the alliance. The success of the hedging program is evaluated from mean-variance and cash-flow perspectives. / Master of Science

Abstract The thesis is addressing the inventory valuation method called moving average and how this inventory method handles exchange rate differences. Intentions of the study is also to highlight differences and similarities between the two methods standard cost and moving average. This study fills an existing gap in science regarding pros and cons with the moving average method which made the topic very interesting.  It also has strong practical contribution regarding possible benefits and problems of relevance to companies that have intentions of implementing moving average on their inventory. The relationships between foreign exchange rate risks and inventory leads to the formulated research question for this thesis: What are the effects of currency movements in the cost of goods sold from an inventory valued at moving average method? Based on the technical problem statement was a constructive approach and interpretive standpoint considered best suited for the study. The gathering of data was conducted by using a qualitative research strategy. Three different topics are used in the theoretical frame; inventory valuation, exchange rates and hedging. The theoretical frame describes the accounting standards behind inventory valuation and exchange rates, as well as the theories addressed. Third and final topic hedging is about how to manage exchange rate exposures using different hedging techniques. The in-depth investigation was made for four business units with inventories valued according to the moving average method. Sampling was divided into two parts one for the companies and another choosing respondents. Selection of companies was a convenient sample within the non-probability samples used and the respondents were selected using a snowball sample. Semi-structured interviews were conducted with nine respondents. Both the empirical- and analysis chapter follows the same three topics as the theory structure and the empirical answers are divided into companies to facilitate the comparison. A short summary of the analysis is that moving average is most suitable for inventories with; high inventory turnovers, sales from shelf and stable costs. There is a need to identify input costs to manage exchange rate differences correctly. The final part about hedging showed that different exposures need different hedging techniques. Forward contracts were the most common financial instrument used for hedging transaction exposures. Input risks also identified as an economic risk is one of the hardest to manage. This study has showed that effects from exchange rate fluctuations affect the moving average inventory value different than other inventory models. The input currencies need to be identified and separated from the sales currencies otherwise there is a potential risk to make wrong decisions.

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This dissertation investigates the interactive or joint influence of autocorrelative processes (autoregressive-AR, moving average-MA, and autoregressive moving average-ARMA) and sample weights present in a longitudinal panel data set. Specifically, to what extent are the sample estimates influenced when autocorrelation (which is usually present in a panel data having correlated observations and errors) and sample weights (complex sample design feature used in longitudinal data having multi-stage sampling design) are modeled versus when they are not modeled or either one of them is taken into account. The current study utilized a Monte Carlo simulation design to vary the type and magnitude of autocorrelative processes and sample weights as factors incorporated in growth or latent curve models to evaluate the effect on sample latent curve estimates (mean intercept, mean slope, intercept variance, slope variance, and intercept slope correlation). Various latent curve models with weights or without weights were specified with an autocorrelative process and then fitted to data sets having either the AR, MA or ARMA process. The relevance and practical importance of the simulation results were ascertained by testing the joint influence of autocorrelation and weights on the Early Childhood Longitudinal Study for Kindergartens (ECLS-K) data set which is a panel data set having complex sample design features. The results indicate that autocorrelative processes and weights interact with each other as sources of error to a statistically significant degree. Accounting for just the autocorrelative process without weights or utilizing weights while ignoring the autocorrelative process may lead to bias in the sample estimates particularly in large-scale datasets in which these two sources of error are inherently embedded. The mean intercept and mean slope of latent curve models without weights was consistently underestimated when fitted to data sets having AR, MA or ARMA process. On the other hand, the intercept variance, intercept slope, and intercept slope correlation were overestimated for latent curve models with weights. However, these three estimates were not accurate as the standard errors associated with them were high. In addition, fit indices, AR and MA estimates, parsimony of the model, behavior of sample latent curve estimates, and interaction effects between autocorrelative processes and sample weights should be assessed for all the models before a particular model is deemed as most appropriate. If the AR estimate is high and MA estimate is low for a LCAR model than the other models that are fitted to a data set having sample weights and the fit indices are in the acceptable cut-off range, then the data set has a higher likelihood of having an AR process between the observations. If the MA estimate is high and AR estimate is low for a LCMA model than the other models that are fitted to a data set having sample weights and the fit indices are in the acceptable cut-off range, then the data set has a higher likelihood of having an MA process between the observations. If both AR and MA estimates are high for a LCARMA model than the other models that are fitted to a data set having sample weights and the fit indices are in the acceptable cut-off range, then the data set has a higher likelihood of having an ARMA process between the observations. The results from the current study recommends that biases from both autocorrelation and sample weights needs to be simultaneously modeled to obtain accurate estimates. The type of autocorrelation (AR, MA or ARMA), magnitude of autocorrelation, and sample weights influences the behavior of estimates and all the three facets should be carefully considered to correctly interpret the estimates especially in the context of measuring growth or change in the variable(s) of interest over time in large-scale longitudinal panel data sets.

Aldrig har det varit lika aktuellt med hållbar teknologi som idag. Behovet av bättre miljöpåverkan inom alla områden har snabbt ökat och energikonsumtionen är ett av dem. En enkel lösning för automatisk kontroll av energikonsumtionen i smarta hem är genom mjukvara. Med dagens IoT teknologi och maskinlärningsmodeller utvecklas den mjukvarubaserade hållbara livsstilen allt mer. För att kontrollera ett hushålls energikonsumption måste plötsligt avvikande beteenden detekteras och regleras för att undvika onödig konsumption. Detta examensarbete använder en tidsserie av temperaturdata för att implementera detektering av anomalier. Fyra modeller implementerades och testades; en linjär regressionsmodell, Pandas EWM funktion, en EWMA modell och en PEWMA modell. Varje modell testades genom att använda dataset från nio olika lägenheter, från samma tidsperiod. Därefter bedömdes varje modell med avseende på Precision, Recall och F-measure, men även en ytterligare bedömning gjordes för linjär regression med R^2-score. Resultaten visar att baserat på noggrannheten hos varje modell överträffade PEWMA de övriga modellerna. EWMA modeller var något bättre än den linjära regressionsmodellen, följt av Pandas egna EWM modell. / Today's society has become more aware of its surroundings and the focus has shifted towards green technology. The need for better environmental impact in all areas is rapidly growing and energy consumption is one of them. A simple solution for automatically controlling the energy consumption of smart homes is through software. With today's IoT technology and machine learning models the movement towards software based ecoliving is growing. In order to control the energy consumption of a household, sudden abnormal behavior must be detected and adjusted to avoid unnecessary consumption. This thesis uses a time-series data set of temperature data for implementation of anomaly detection. Four models were implemented and tested; a Linear Regression model, Pandas EWM function, an exponentially weighted moving average (EWMA) model and finally a probabilistic exponentially weighted moving average (PEWMA) model. Each model was tested using data sets from nine different apartments, from the same time period. Then an evaluation of each model was conducted in terms of Precision, Recall and F-measure, as well as an additional evaluation for Linear Regression, using R^2 score. The results of this thesis show that in terms of accuracy, PEWMA outperformed the other models. The EWMA model was slightly better than the Linear Regression model, followed by the Pandas EWM model.

Increasing sophistication of exchange traded fund (ETF) indexation methods required that a comparison be drawn between various methodologies. A performance and risk evaluation of four pre-selected ETF indexation categories were conducted to establish the diversification benefits that each contain. Fundamentally weighted, equally weighted and leveraged ETFs were compared to traditional market capitalisation weighted ETFs on the basis of risk and return. While a literature review presented the theory on ETFs and the various statistical measures used for this study, the main findings were obtained empirically from a sample of South African and American ETFs. Several risk-adjusted performance measures were employed to assess the risk and return of each indexation category. Special emphasis was placed on the Omega ratio due to the unique interpretation of the return series‟ distribution characteristics. The risk of each ETF category was evaluated using the exponentially weighted moving average (EWMA), while the diversification potential was determined by means of a regression analysis based on the single index model. According to the findings, fundamentally weighted ETFs perform the best during an upward moving market when compared by standard risk-adjusted performance measures. However, the Omega ratio analysis revealed the inherent unsystematic risk of alternatively indexed ETFs and ranked market capitalisation weighted ETFs as the best performing category. Equal weighted ETFs delivered consistently poor rankings, while leveraged ETFs exhibited a high level of risk associated with the amplified returns of this category. The diversification measurement concurred with the Omega ratio analysis and highlighted the market capitalisation weighted ETFs to be the most diversified ETFs in the selection. Alternatively indexed ETFs consequently deliver higher absolute returns by incurring greater unsystematic risk, while simultaneously reducing the level of diversification in the fund. / MCom (Risk Management), North-West University, Vaal Triangle Campus, 2014

Increasing sophistication of exchange traded fund (ETF) indexation methods required that a comparison be drawn between various methodologies. A performance and risk evaluation of four pre-selected ETF indexation categories were conducted to establish the diversification benefits that each contain. Fundamentally weighted, equally weighted and leveraged ETFs were compared to traditional market capitalisation weighted ETFs on the basis of risk and return. While a literature review presented the theory on ETFs and the various statistical measures used for this study, the main findings were obtained empirically from a sample of South African and American ETFs. Several risk-adjusted performance measures were employed to assess the risk and return of each indexation category. Special emphasis was placed on the Omega ratio due to the unique interpretation of the return series‟ distribution characteristics. The risk of each ETF category was evaluated using the exponentially weighted moving average (EWMA), while the diversification potential was determined by means of a regression analysis based on the single index model. According to the findings, fundamentally weighted ETFs perform the best during an upward moving market when compared by standard risk-adjusted performance measures. However, the Omega ratio analysis revealed the inherent unsystematic risk of alternatively indexed ETFs and ranked market capitalisation weighted ETFs as the best performing category. Equal weighted ETFs delivered consistently poor rankings, while leveraged ETFs exhibited a high level of risk associated with the amplified returns of this category. The diversification measurement concurred with the Omega ratio analysis and highlighted the market capitalisation weighted ETFs to be the most diversified ETFs in the selection. Alternatively indexed ETFs consequently deliver higher absolute returns by incurring greater unsystematic risk, while simultaneously reducing the level of diversification in the fund. / MCom (Risk Management), North-West University, Vaal Triangle Campus, 2014

With few previous data and literature based on the South African banking sector, the key aim of this study was to contribute further results concerning the effect of operational loss events on the reputation of South African banks. The main distinction between this study and previous empirical research is that a small sample of South African banks listed on the JSE, between 2000 and 2014 was used. Insurance companies fell outside the scope of the study. The study primarily focused on identifying reputational risk among Regal Treasury Bank, Saambou Bank, African Bank and Standard Bank. The events announced by these banks occurred between 2000 and 2014. The precise date of the announcement of the operational events was also determined. Stock price data were collected for those banks that had unanticipated operational loss announcements (i.e. the event). Microsoft Excel models applied to the reputational loss as the difference between the operational loss announcement and the loss in the stock returns of the selected banks. The results indicated significant negative abnormal returns on the announcement day for three of the four banks. For one of the banks it was assumed that the operational loss was not significant enough to cause reputational risk. The event methodology similar to previous literature, furthermore examined the behaviour of return volatility after specific operational loss events using the sample of banks. The study further aimed at making two contributions. Firstly, to analyse return volatility after operational loss announcements had been made among South African banks, and secondly, to compare the sample of affected banks with un-affected banks to further identify whether these events spilled over into the banking industry and the market. The volatility of these four banks were compared to three un-affected South African banks. The results found that the operational loss events for Regal Treasury Bank and Saambou Bank had no influence on the unaffected banks. However the operational loss events for African Bank and Standard Bank influenced the sample of unaffected banks and the Bank Index, indicating systemic risk.