Forecasting volatility with precision in financial market is very important. This paper examines the use of various forms of GARCH models for forecasting volatility. Three financial data sets from Japan (NIKKEI 225 index), the United States (Standard & Poor 500) and Germany (DAX index) are considered. A number of GARCH models, such as EGARCH, IGARCH, TGARCH, PGARCH and QGARCH models with normal distribution and student’s t distribution are used to fit the data sets and to forecast volatility. The Maximum Likelihood method and the Bayesian approach are used to estimate the parameters in the family of the GARCH models. The results show that the QGARCH model under student’s t distribution is the precise model for the NIKKEI 225 index in terms of fitting the data and forecasting volatility. The TGARCH under the student’s t distribution fits the S&P 500 index data better while the traditional GARCH model under the same distribution performs better in forecasting volatility. The PGARCH with student’s t distribution is the precise model for the DAX index in terms of fitting the data and forecasting volatility. / Department of Mathematical Sciences

This research focuses on developing a crop decision planning model to help farmers make decisions for an upcoming crop year. The decisions consist of which crops to plant, the amount of land to allocate to each crop, when to grow, when to harvest, and when to sell. The objective is to maximize the overall profit subject to available resources under yield and price uncertainties. To help achieve this objective, we develop yield and price forecasting models to estimate the probable outcomes of these uncertain factors. The output from both forecasting models are incorporated into the crop decision planning model which enables the farmers to investigate and analyze the possible scenarios and eventually determine the appropriate decisions for each situation. This dissertation has three major components, yield forecasting, price forecasting, and crop decision planning. For yield forecasting, we propose a crop-weather regression model under a semiparametric framework. We use temperature and rainfall information during the cropping season and a GDP macroeconomic indicator as predictors in the model. We apply a functional principal components analysis technique to reduce the dimensionality of the model and to extract meaningful information from the predictors. We compare the prediction results from our model with a series of other yield forecasting models. For price forecasting, we develop a futures-based model which predicts a cash price from futures price and commodity basis. We focus on forecasting the commodity basis rather than the cash price because of the availability of futures price information and the low uncertainty of the commodity basis. We adopt a model-based approach to estimate the density function of the commodity basis distribution, which is further used to estimate the confidence interval of the commodity basis and the cash price. Finally, for crop decision planning, we propose a stochastic linear programming model, which provides the optimal policy. We also develop three heuristic models that generate a feasible solution at a low computational cost. We investigate the robustness of the proposed models to the uncertainties and prior probabilities. A numerical study of the developed approaches is performed for a case of a representative farmer who grows corn and soybean in Illinois.

Bibliography / Thesis (MPhil (Journalism))--University of Stellenbosch, 2010.

The aim of this study is to develop novel forecasting methodologies. The applications of our proposed models lie in two different areas: macroeconomics and energy. Though we consider two very different applications, the common underlying theme of this thesis is to develop novel methodologies that are not only accurate, but are also parsimonious. For macroeconomic time series, we focus on generating forecasts for the US Gross National Product (GNP). The contribution of our study on macroeconomic forecasting lies in proposing a novel nonlinear and nonparametric method, called weighted random analogue prediction (WRAP) method. The out-of-sample forecasting ability of WRAP is evaluated by employing a range of different performance scores, which measure its accuracy in generating both point and density forecasts. We show that WRAP outperforms some of the most commonly used models for forecasting the GNP time series. For energy, we focus on two different applications: (1) Generating accurate short-term forecasts for the total electricity demand (load) for Great Britain. (2) Modelling Irish electricity smart meter data (consumption) for both residential consumers and small and medium-sized enterprises (SMEs), using methods based on kernel density (KD) and conditional kernel density (CKD) estimation. To model load, we propose methods based on a commonly used statistical dimension reduction technique, called singular value decomposition (SVD). Specifically, we propose two novel methods, namely, discount weighted (DW) intraday and DW intraweek SVD-based exponential smoothing methods. We show that the proposed methods are competitive with some of the most commonly used models for load forecasting, and also lead to a substantial reduction in the dimension of the model. The load time series exhibits a prominent intraday, intraweek and intrayear seasonality. However, most existing studies accommodate the ‘double seasonality’ while modelling short-term load, focussing only on the intraday and intraweek seasonal effects. The methods considered in this study accommodate the ‘triple seasonality’ in load, by capturing not only intraday and intraweek seasonal cycles, but also intrayear seasonality. For modelling load, we also propose a novel rule-based approach, with emphasis on special days. The load observed on special days, e.g. public holidays, is substantially lower compared to load observed on normal working days. Special day effects have often been ignored during the modelling process, which leads to large forecast errors on special days, and also on normal working days that lie in the vicinity of special days. The contribution of this study lies in adapting some of the most commonly used seasonal methods to model load for both normal and special days in a coherent and unified framework, using a rule-based approach. We show that the post-sample error across special days for the rule-based methods are less than half, compared to their original counterparts that ignore special day effects. For modelling electricity smart meter data, we investigate a range of different methods based on KD and CKD estimation. Over the coming decade, electricity smart meters are scheduled to replace the conventional electronic meters, in both US and Europe. Future estimates of consumption can help the consumer identify and reduce excess consumption, while such estimates can help the supplier devise innovative tariff strategies. To the best of our knowledge, there are no existing studies which focus on generating density forecasts of electricity consumption from smart meter data. In this study, we evaluate the density, quantile and point forecast accuracy of different methods across one thousand consumption time series, recorded from both residential consumers and SMEs. We show that the KD and CKD methods accommodate the seasonality in consumption, and correctly distinguish weekdays from weekends. For each application, our comprehensive empirical comparison of the existing and proposed methods was undertaken using multiple performance scores. The results show strong potential for the models proposed in this thesis.

Mercado Preditivo (MP) é uma ferramenta que utiliza o mecanismo de preço de mercado para agregar informações dispersas em um grande grupo de pessoas, visando à geração de previsões sobre assuntos de interesse. Trata-se de um método de baixo custo, capaz de gerar previsões de forma contínua e que não exige amostras probabilísticas. Há diversas aplicações para esses mercados, sendo que uma das principais é o prognóstico de resultados eleitorais. Este estudo analisou evidências empíricas da eficácia de um Mercado Preditivo no Brasil, criado para fazer previsões sobre os resultados das eleições gerais do ano de 2014, sobre indicadores econômicos e sobre os resultados de jogos do Campeonato Brasileiro de futebol. A pesquisa teve dois grandes objetivos: i) desenvolver e avaliar o desempenho de um MP no contexto brasileiro, comparando suas previsões em relação a métodos alternativos; ii) explicar o que motiva as pessoas a participarem do MP, especialmente quando há pouca ou nenhuma interação entre os participantes e quando as transações são realizadas com uma moeda virtual. O estudo foi viabilizado por meio da criação da Bolsa de Previsões (BPrev), um MP online que funcionou por 61 dias, entre setembro e novembro de 2014, e que esteve aberto à participação de qualquer usuário da Internet no Brasil. Os 147 participantes registrados na BPrev efetuaram um total de 1.612 transações, sendo 760 no tema eleições, 270 em economia e 582 em futebol. Também foram utilizados dois questionários online para coletar dados demográficos e percepções dos usuários. O primeiro foi aplicado aos potenciais participantes antes do lançamento da BPrev (302 respostas válidas) e o segundo foi aplicado apenas aos usuários registrados, após dois meses de experiência de uso da ferramenta (71 respostas válidas). Com relação ao primeiro objetivo, os resultados sugerem que Mercados Preditivos são viáveis no contexto brasileiro. No tema eleições, o erro absoluto médio das previsões do MP na véspera do pleito foi de 3,33 pontos percentuais, enquanto o das pesquisas de opinião foi de 3,31. Considerando todo o período em que o MP esteve em operação, o desempenho dos dois métodos também foi parecido (erro absoluto médio de 4,20 pontos percentuais para o MP e de 4,09 para as pesquisas). Constatou-se também que os preços dos contratos não são um simples reflexo dos resultados das pesquisas, o que indica que o mercado é capaz de agregar informações de diferentes fontes. Há potencial para o uso de MPs em eleições brasileiras, principalmente como complemento às metodologias de previsão mais tradicionais. Todavia, algumas limitações da ferramenta e possíveis restrições legais podem dificultar sua adoção. No tema economia, os erros foram ligeiramente maiores do que os obtidos com métodos alternativos. Logo, um MP aberto ao público geral, como foi o caso da BPrev, mostrou-se mais indicado para previsões eleitorais do que para previsões econômicas. Já no tema futebol, as previsões do MP foram melhores do que o critério do acaso, mas não houve diferença significante em relação a outro método de previsão baseado na análise estatística de dados históricos. No que diz respeito ao segundo objetivo, a análise da participação no MP aponta que motivações intrínsecas são mais importantes para explicar o uso do que motivações extrínsecas. Em ordem decrescente de relevância, os principais fatores que influenciam a adoção inicial da ferramenta são: prazer percebido, aprendizado percebido, utilidade percebida, interesse pelo tema das previsões, facilidade de uso percebida, altruísmo percebido e recompensa percebida. Os indivíduos com melhor desempenho no mercado são mais propensos a continuar participando. Isso sugere que, com o passar do tempo, o nível médio de habilidade dos participantes tende a crescer, tornando as previsões do MP cada vez melhores. Os resultados também indicam que a prática de incluir questões de entretenimento para incentivar a participação em outros temas é pouco eficaz. Diante de todas as conclusões, o MP revelou-se como potencial técnica de previsão em variados campos de investigação. / Prediction Market (PM) is a tool which uses the market price mechanism to aggregate information scattered in a large group of people, aiming at generating predictions about matters of interest. It is a low cost method, able to generate forecasts continuously and it does not require random samples. There are several applications for these markets and one of the main ones is the prognosis of election outcomes. This study analyzed empirical evidences on the effectiveness of Prediction Markets in Brazil, regarding forecasts about the outcomes of the general elections in the year of 2014, about economic indicators and about the results of the Brazilian Championship soccer games. The research had two main purposes: i) to develop and evaluate the performance of PMs in the Brazilian context, comparing their predictions to the alternative methods; ii) to explain what motivates people´s participation in PMs, especially when there is little or no interaction among participants and when the trades are made with a virtual currency (play-money). The study was made feasible by means of the creation of a prediction exchange named Bolsa de Previsões (BPrev), an online marketplace which operated for 61 days, from September to November, 2014, being open to the participation of any Brazilian Internet user. The 147 participants enrolled in BPrev made a total of 1,612 trades, with 760 on the election markets, 270 on economy and 582 on soccer. Two online surveys were also used to collect demographic data and users´ perceptions. The first one was applied to potential participants before BPrev launching (302 valid answers) and the second was applied only to the registered users after two-month experience in tool using (71 valid answers). Regarding the first purpose, the results suggest Prediction Markets to be feasible in the Brazilian context. On the election markets, the mean absolute error of PM predictions on the eve of the elections was of 3.33 percentage points whereas the one of the polls was of 3.31. Considering the whole period in which BPrev was running, the performance of both methods was also similar (PM mean absolute error of 4.20 percentage points and poll´s 4.09). Contract prices were also found as not being a simple reflection of poll results, indicating that the market is capable to aggregate information from different sources. There is scope for the use of PMs in Brazilian elections, mainly as a complement of the most traditional forecasting methodologies. Nevertheless, some tool limitations and legal restrictions may hinder their adoption. On markets about economic indicators, the errors were slightly higher than those obtained by alternative methods. Therefore, a PM open to general public, as in the case of BPrev, showed as being more suitable to electoral predictions than to economic ones. Yet, on soccer markets, PM predictions were better than the criterion of chance although there had not been significant difference in relation to other forecasting method based on the statistical analysis of historical data. As far as the second purpose is concerned, the analysis of people´s participation in PMs points out intrinsic motivations being more important in explaining their use than extrinsic motivations. In relevance descending order, the principal factors that influenced tool´s initial adoption are: perceived enjoyment, perceived learning, perceived usefulness, interest in the theme of predictions, perceived ease of use, perceived altruism and perceived reward. Individuals with better performance in the market are more inclined to continue participating. This suggests that, over time, participants´ average skill level tends to increase, making PM forecasts better and better. Results also indicate that the practice of creating entertainment markets to encourage participation in other subjects is ineffective. Ratifying all the conclusions, PM showed as being a prediction potential technique in a variety of research fields.

Forecasts of hydrological information are vital for many of society's functions. Availability of water is a requirement for any civilization, and this necessitates quantitative estimates of water for effective resource management. The research in this dissertation will focus on the forecasting of hydrological quantities, with emphasis on times of anomalously low water availability, commonly referred to as droughts. Of particular focus is the quantification of uncertainty in hydrological forecasts, and the factors that affect that uncertainty. With this focus, Bayesian methods, including ensemble data assimilation and multi-model combinations, are utilized to develop a probabilistic forecasting system. This system is applied to the upper Colorado River Basin for water supply and drought forecast analysis. This dissertation examines further advancements related to the identification of drought intensity. Due to the reliance of drought forecasting on measures of the magnitude of a drought event, it is imperative that these measures be highly accurate. In order to quantify drought intensity, hydrologists typically use statistical indices, which place observed hydrological deficiencies within the context of historical climate. Although such indices are a convenient framework for understanding the intensity of a drought event, they have obstacles related to non-stationary climate, and non-uniformly distributed input variables. This dissertation discusses these shortcomings, demonstrates some errors that conventional indices may lead to, and then proposes a movement towards physically-based indices to overcome these issues. A final advancement in this dissertation is an examination of the sensitivity of hydrological forecasts to initial conditions. Although this has been performed in many recent studies, the experiment here takes a more detailed approach. Rather than determining the lead time at which meteorological forcing becomes dominant with respect to initial conditions, this study quantifies the lead time at which the forecast becomes entirely insensitive to initial conditions, and estimating the rate at which the forecast loses sensitivity to initial conditions. A primary goal with this study is to examine the recovery of drought, which is related to the loss of sensitivity to below average initial moisture conditions over time. Through this analysis, it is found that forecasts are sensitive to initial conditions at greater lead times than previously thought, which has repercussions for development of forecast systems.

Recent water scarcities across the southwestern U.S. with severe effects on the living environment inspire the development of new methodologies to achieve reliable drought forecasting in seasonal scale. Reliable forecast of hydrologic variables, in general, is a preliminary requirement for appropriate planning of water resources and developing effective allocation policies. This study aims at developing new techniques with specific probabilistic features to improve the reliability of hydrologic forecasts, particularly the drought forecasts. The drought status in the future is determined by certain hydrologic variables that are basically estimated by the hydrologic models with rather simple to complex structures. Since the predictions of hydrologic models are prone to different sources of uncertainties, there have been several techniques examined during past several years which generally attempt to combine the predictions of single (multiple) hydrologic models to generate an ensemble of hydrologic forecasts addressing the inherent uncertainties. However, the imperfect structure of hydrologic models usually lead to systematic bias of hydrologic predictions that further appears in the forecast ensembles. This study proposes a post-processing method that is applied to the raw forecast of hydrologic variables and can develop the entire distribution of forecast around the initial single-value prediction. To establish the probability density function (PDF) of the forecast, a group of multivariate distribution functions, the so-called copula functions, are incorporated in the post-processing procedure. The performance of the new post-processing technique is tested on 2500 hypothetical case studies and the streamflow forecast of Sprague River Basin in southern Oregon. Verified by some deterministic and probabilistic verification measures, the method of Quantile Mapping as a traditional post-processing technique cannot generate the qualified forecasts as comparing with the copula-based method. The post-processing technique is then expanded to exclusively study the drought forecasts across the different spatial and temporal scales. In the proposed drought forecasting model, the drought status in the future is evaluated based on the drought status of the past seasons while the correlations between the drought variables of consecutive seasons are preserved by copula functions. The main benefit of the new forecast model is its probabilistic features in analyzing future droughts. It develops conditional probability of drought status in the forecast season and generates the PDF and cumulative distribution function (CDF) of future droughts given the past status. The conditional PDF can return the highest probable drought in the future along with an assessment of the uncertainty around that value. Using the conditional CDF for forecast season, the model can generate the maps of drought status across the basin with particular chance of occurrence in the future. In a different analysis of the conditional CDF developed for the forecast season, the chance of a particular drought in the forecast period can be approximated given the drought status of earlier seasons. The forecast methodology developed in this study shows promising results in hydrologic forecasts and its particular probabilistic features are inspiring for future studies.

Typescript (photocopy). / Digitized by Kansas Correctional Industries

Typescript (photocopy). / Digitized by Kansas Correctional Industries

Typescript (photocopy). / Digitized by Kansas Correctional Industries