The dissertation deals with prediction of crude oil price and is tailor-made for such companies which are heavily crude oil related. The main dissertation target is to make sure that such companies can get ready for price changes and safeguard themselves against negative consequences. Crude oil prices are the main factor which affects prices of such final products as petrol. It is a well known fact that quantitative predictions are not reliable and all those who are forced to real on such vague data set for their decision-making are reluctant to use them. That’s how we would like to have at least the correct trend information. The dissertation introduces some concepts originally developed within artificial intelligence theory for the crude oil predictions. Specifically common sense algorithms and qualitative interpretation of some aspects of theory of chaos are the main contribution towards expanding of available prediction tools described by the dissertation. A systematic analysis of a sequence of qualitative solutions is the key part of the dissertation.

In this work we want to examine selected models with nonlinear volatility and their properties. At the beginning we define models with non-constant variance, especially ARCH, GARCH and EGARCH models. Then we study the probability distributions that are mainly used in the EGARCH model. Then we focus on the EGARCH model, describe the conditions for stationarity and invertibility of the model, define diagnostic tests and QMLE estimates of parameters. In the last chapter we perform simulation studies of the selected models and their application to real data. 1

Thesis (MComm (Business Management))--University of Stellenbosch, 2007. / ENGLISH ABSTRACT: his study aims to investigate whether the phenomena found by Shnoll et al. when applying histogram pattern analysis techniques to stochastic processes from chemistry and physics are also present in financial time series, particularly exchange rate and index data. The phenomena are related to fine structure of non-smoothed frequency distributions drawn from statistically insufficient samples of changes and their patterns in time. Shnoll et al. use the notion of macroscopic fluctuations to explain the behaviour of sequences of histograms. Histogram patterns in time adhere to several laws that could not be detected when using time series analysis methods. In this study general approaches are reviewed that may be used to model financial markets and the volatility of price processes in particular. Special emphasis is placed on the modelling of highfrequency data sets and exchange rate data. Following previous studies of the Shnoll phenomena from other fields, different steps of the histogram sequence analysis are carried out to determine whether the findings of Shnoll et al. could also be applied to financial market data. The findings of this thesis widen the understanding of time varying volatility and can aid in financial risk measurement and management. Outcomes of the study include an investigation of time series characteristics in terms of the formation of discrete states, the detection of the near zone effect as proclaimed by Shnoll et al., the periodic recurrence of histogram shapes as well as the synchronous variation in data sets measured in the same time intervals.

The last few years have witnessed an exponential increase in the availability and use of financial market data, which is sampled at increasingly high frequencies. Extracting useful information about the dependency structure of a system from these multivariate data streams has numerous practical applications and can aid in improving our understanding of the driving forces in the global financial markets. These large and noisy data sets are highly non-Gaussian in nature and require the use of efficient and accurate interaction measurement approaches for their analysis in a real-time environment. However, most frequently used measures of interaction have certain limitations to their practical use, such as the assumption of normality or computational complexity. This thesis has two major aims; firstly, to address this lack of availability of suitable methods by presenting a set of approaches to dynamically measure symmetric and asymmetric interactions, i.e. causality, in multivariate non-Gaussian signals in a computationally efficient (online) framework, and secondly, to make use of these approaches to analyse multivariate financial time series in order to extract interesting and practically useful information from financial data. Most of our proposed approaches are primarily based on independent component analysis, a blind source separation method which makes use of higher-order statistics to capture information about the mixing process which gives rise to a set of observed signals. Knowledge about this information allows us to investigate the information coupling dynamics, as well as to study the asymmetric flow of information, in multivariate non-Gaussian data streams. We extend our multivariate interaction models, using a variety of statistical techniques, to study the scale-dependent nature of interactions and to analyse dependencies in high-dimensional systems using complex coupling networks. We carry out a detailed theoretical, analytical and empirical comparison of our proposed approaches with some other frequently used measures of interaction, and demonstrate their comparative utility, efficiency and accuracy using a set of practical financial case studies, focusing primarily on the foreign exchange spot market.

This thesis focuses on estimating parameters of appropriate model for daily returns using the Markov Chain Monte Carlo method (MCMC) and Bayesian statistics. We describe MCMC methods, such as Gibbs sampling and Metropolis- Hastings algorithm and their basic properties. After that, we introduce different financial models. Particularly we focus on the lognormal autoregressive model. Later we theoretically apply Gibbs sampling to lognormal autoregressive model using principles of Bayesian statistics. Afterwards, we analyze procedu- res, that we used in simulations of posterior distribution using Gibbs sampling. Finally, we present processed output of both simulated and real data analysis.

Sabe-se que, na literatura, existem muitos modelos para se fazer previsão para séries temporais financeiras. Sabe-se também que não há um modelo perfeito e que os mais utilizados atualmente são os modelos de redes neurais recorrentes e os da família GARCH. Referências internacionais apontam que existe uma técnica de medição de uma janela temporal para se identificar o tipo de comportamento existente em uma série temporal; tal técnica é conhecida como Expoente de Hurst. É uma medida que qualifica a série como persistente ou anti-persistente. Este trabalho analisou se o Expoente de Hurst, interfere na qualidade das previsões feitas com o modelo de redes neurais recorrentes com e sem o uso do filtro de ondaletas, utilizando os preços diários das principais commodities, ações negociadas no mercado e a taxa de câmbio. no período de janeiro de 1998 a dezembro de 2010. Com a pesquisa observa-se, na maioria dos casos, há uma possível melhora na qualidade das previsões para as séries antipersistentes. / It is known that there are a lot of models to forecast financial time series. It is known, also, that there is not a perfect model and the most used nowadays are the Recurrent Neural Network models and those from the GARCH family. International references point to a technique of measurement using windowing in order to identify the kind of behavior that is present in time series. This technique is known as Hurst Exponent. It is a measure that qualifies the time series as persistent or anti-persistent. This work analyzed if the Hurst Exponent interferes in the quality of the forecasts made with the Neural Network models with and without the wavelet filter, using the main commodities, stock prices, Ibovespa index and the Dollar/Real exchange rate in the period ranging from January 1998 to December 2010. The initial conclusions concerning the models worked out are positives.

Neste trabalho estudamos diferentes variantes dos modelos GARCH quando consideramos a chegada da informação heterogênea sob a forma de dados de alta freqüência. Este tipo de modelos, conhecidos como HARCH(n), foram introduzidos por Muller et al. (1997). Para entender a necessidade de incorporar esta característica da heterogeneidade da informação, estudamos o problema da agregação temporal para processos GARCH e a modelagem destes em dados de alta freqüência e veremos quais são as desvantagens destes modelos e o porquê da necessidade de corrigi-lo. Propusemos um novo modelo que leva em conta a heterogeneidade da informação do mercado financeiro e a memória longa da volatilidade, generalizando assim o modelo proposto por Müller et al.(1997), e estudamos algumas das propriedades teóricas do modelo proposto. Utilizamos estimação via máxima verossimilhança e amostrador de Griddy-Gibbs, e para avaliar o desempenho destes métodos realizamos diversas simulações. Também fizemos aplicações a duas séries de alta freqüência, a taxa de câmbio Euro- Dólar e o índice Ibovespa. Uma modificação ao algoritmo de Griddy-Gibbs foi proposta, para ter uma janela móvel de pontos, para a estimação das distribuições condicionais, a cada iteração. Este procedimento foi validado pela proximidade das estimações com a técnica de máxima verossimilhança. Disponibilizaremos algumas bibliotecas para o pacote S-Plus em que as análises descritas neste trabalho poderão ser reproduzidas. Informações relativas a tais bibliotecas estarão disponíveis na página Web http://www.ime.usp.br/~ruilova. / In this work we study different variants of GARCH models to analyze the arrival of heterogeneous information in high frequency data. These models, known as HARCH(*n*) models, were introduced by Müller et al.(1997). To understand the necessity to incorporate this characteristic, heterogeneous information, we study temporal aggregation on GARCH processes for high frequency data, and show some problems in the application of these models and the reason why it is necessary to develop new models. We propose a new model, that incorporates the heterogeneous information present in the financial market and the long memory of the volatility, generalizing the model considered by Müller et al.(1997). We propose to estimate the model via maximum likelihood and Griddy-Gibbs sampler. To assess the performance of the suggested estimation procedures we perform some simulations and apply the methodology to two time series, namely the foreign exchange rate Euro-Dollar and the series of the Ibovespa index. A modification of the algorithm of Griddy-Gibbs sampler was proposed to have a grid of points in a mobile window, to estimate the condicional distributions, in each iteration. This was validated by the similar results between maximum likelihood and Griddy-Gibbs sampler estimates obtained. We implemented the methods described in this work creating some libraries for the SPlus package. Information concerning these libraries is available in the Web page http://www.ime.usp.br/~ruilova.

The evolution of big data has led to financial time series becoming increasingly complex, noisy, non-stationary and nonlinear. Takens theorem can be used to analyze and forecast nonlinear time series, but even small amounts of noise can hopelessly corrupt a Takens approach. In contrast, Singular Spectrum Analysis is an excellent tool for both forecasting and noise reduction. Fortunately, it is possible to combine the Takens approach with Singular Spectrum analysis (SSA), and in fact, estimation of key parameters in Takens theorem is performed with Singular Spectrum Analysis. In this thesis, we combine the denoising abilities of SSA with the Takens theorem approach to make the manifold reconstruction outcomes of Takens theorem less sensitive to noise. In particular, in the course of performing the SSA on a noisy time series, we branch of into a Takens theorem approach. We apply this approach to a variety of noisy time series.

Doctor of Philosophy / This thesis is based on research on financial time series analysis using pattern recognition methods. The first part of this research focuses on univariate time series analysis using different pattern recognition methods. First, probabilities of basic patterns are used to represent the features of a section of time series. This feature can remove noise from the time series by statistical probability. It is experimentally proven that this feature is successful for pattern repeated time series. Second, a multiscale Gaussian gravity as a pattern relationship measurement which can describe the direction of the pattern relationship is introduced to pattern clustering. By searching for the Gaussian-gravity-guided nearest neighbour of each pattern, this clustering method can easily determine the boundaries of the clusters. Third, a method that unsupervised pattern classification can be transformed into multiscale supervised pattern classification by multiscale supervisory time series or multiscale filtered time series is presented. The second part of this research focuses on multivariate time series analysis using pattern recognition. A systematic method is proposed to find the independent variables of a group of share prices by time series clustering, principal component analysis, independent component analysis, and object recognition. The number of dependent variables is reduced and the multivariate time series analysis is simplified by time series clustering and principal component analysis. Independent component analysis aims to find the ideal independent variables of the group of shares. Object recognition is expected to recognize those independent variables which are similar to the independent components. This method provides a new clue to understanding the stock market and to modelling a large time series database.

The thesis "Four Essays on the Econometric Modelling of Volatility and Durations" consists of four research papers in the area of financial econometrics on topics of the modelling of financial market volatility and the econometrics of ultra-high-frequency data. The aim of the thesis is to develop new econometric methods for modelling and hypothesis testing in these areas. The second chapter introduces a new model, the time-varying GARCH (TV-GARCH) model, in which volatility has a smooth time-varying structure of either additive or multiplicative type. To characterize smooth changes in the (un)conditional variance we assume that the parameters vary smoothly over time according to the logistic transition function. A data-based modelling technique is used for specifying the parametric structure of the TV-GARCH models. This is done by testing a sequence of hypotheses by Lagrange multiplier tests presented in the chapter. Misspecification tests are also provided for evaluating the adequacy of the estimated model. The third chapter addresses the issue of modelling deterministic changes in the unconditional variance over a long return series. The modelling strategy is illustrated with an application to the daily returns of the Dow Jones Industrial Average (DJIA) index from 1920 until 2003. The empirical results sustain the hypothesis that the assumption of constancy of the unconditional variance is not adequate over long return series and indicate that deterministic changes in the unconditional variance may be associated with macroeconomic factors. In the fourth chapter we propose an extension of the univariate multiplicative TV-GARCH model to the multivariate Conditional Correlation GARCH (CC-GARCH) framework. The variance equations are parameterized such that they combine the long-run and the short-run dynamic behaviour of the volatilities. In this framework, the long-run behaviour is described by the individual unconditional variances, and it is allowed to vary smoothly over time according to the logistic transition function. The effects of modelling the nonstationary variance component are examined empirically in several CC-GARCH models using pairs of seven daily stock return series from the S&P 500 index. The results show that the magnitude of such effect varies across different stock series and depends on the structure of the conditional correlation matrix. An important feature of financial durations is the evidence of a strong diurnal variation over the trading day. In the fifth chapter we propose a new parameterization for describing the diurnal pattern of trading activity. The parametric structure of the diurnal component allows the duration process to change smoothly over the time-of-day according to the logistic transition function. The empirical results suggest that the diurnal variation may not always have the inverted U-shaped pattern for the trade durations as documented in earlier studies.