As an extension of the geometric Brownian motion, a geometric fractional Brownian motion (GFBM) is considered as a stock-price model. The modeled GFBM is compared with empirical Chinese stock prices. Comparisons are performed by considering logarithmic-return densities, autocovariance functions, spectral densities and trajectories. Since logarithmic-return densities of GFBM stock prices are Gaussian and empirical stock logarithmic-returns typically are far from Gaussian, a GFBM model may not be the most suitable stock price model.

Made available in DSpace on 2014-06-11T19:25:31Z (GMT). No. of bitstreams: 0 Previous issue date: 2004-12-20Bitstream added on 2014-06-13T19:32:42Z : No. of bitstreams: 1 favaretto_ab_me_rcla.pdf: 1219340 bytes, checksum: 8add91d75469d4bb5abdc17d48f9449e (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Os sinais analisados são séries temporais de precipitações pluviométricas ou simplesmente denominadas chuvas, que sofrem influências de outras variáveis atmosféricas, como a temperatura, pressão, vento, relevo, posição geográfica, sazonalidade, dentre outras, constituindo um sistema complexo. Estas séries temporais de chuvas, foram obtidas de 48 postos de coleta de dados, com medidas diária, em (mm), de quantidade de chuva, pertencentes a 38 municípios, localizados nas 9 regiões climáticas do Estado de São Paulo, proposto por Monteiro (1973). Os valores do expoente de Hurst, destas séries temporais, foram estimados com o método conhecido como análise R/S, o método utilizando a transformada de Fourier e o método utilizando a transformada de wavelets. A análise R/S e o método utilizando a transformada de Fourier apresentaram resultados equivalentes, mostrando coerência e grande importância na análise de sistemas complexos, objeto deste estudo. O método utilizando a transformada de wavelets, forneceu alguns resultados coerentes, uma grande parte, com resultados superestimados e uma pequena parte, com resultados subestimados, em relação aos outros dois métodos, mostrando-se inadequado para esta análise. / We analyze temporal series associated to pluvial precipitations, best known as rain, The latter depends on temperature, pressure, landscape, location and season, among many other atmospheric variables, thus qualifying as a complex system. These rain's temporal series were obtained from 48 data collection posts, with daily rain measurements (in mm), associated to 38 counties within the nine climatic regions of the State of São Paulo. The values of the time series Hurst exponent, were computed by three methods namely: the R/S analysis method, a Fourier transform and the wavelet transform method. The first two yield coherent results, showing both the consistency and relevance of these methods when applied to complex systems, the main goal of this work. The wavelet method yielded higher and lower values for the Hurst exponent, thus probing the limitations of this method.

A necessidade de antecipar e identificar variações de acontecimentos apontam para uma nova direção nos mercados de bolsa de valores e vem de encontro às análises das oscilações de preços de ativos financeiros. Esta necessidade leva a argumentar sobre novas alternativas na predição de séries temporais financeiras utilizando métodos de aprendizado de máquinas e vários modelos têm sido desenvolvidos para efetuar a análise e a previsão de dados de ativos financeiros. Este trabalho tem por objetivo propor o desenvolvimento de um modelo de previsão adaptativo baseado em um sistema SVR-wavelet híbrido, que integra modelos de wavelets e Support Vector Regression (SVR) na previsão de séries financeiras. O método consiste na utilização da Transformada de Wavelet Discreta (DWT) a fim de decompor dados de séries de ativos financeiros que são utilizados como variáveis de entrada do SVR com o objetivo de prever dados futuros de ativos financeiros. O modelo proposto é aplicado a um conjunto de ativos financeiros do tipo Foreign Exchange Market (FOREX), Mercado Global de Câmbio, obtidos a partir de uma base de conhecimento público. As séries são ajustadas gerando-se novas predições das séries originais, que são comparadas com outros modelos tradicionais tais como o modelo Autorregressivo Integrado de Médias Móveis (ARIMA), o modelo Autorregressivo Fracionário Integrado de Médias Móveis (ARFIMA), o modelo Autorregressivo Condicional com Heterocedasticidade Generalizado (GARCH) e o modelo SVR tradicional com Kernel. Além disso, realizam-se testes de normalidade e de raiz unitária para distribuição não linear, tal como testes de correlação, para constatar que as séries temporais FOREX são adequadas para a comprovação do modelo híbrido SVR-wavelet e posterior comparação com modelos tradicionais. Verifica-se também a aderência ao Expoente de Hurst por meio da estatística de Reescalonamento (R/S). / The necessity to anticipate and identify changes in events points to a new direction in the stock exchange market and reaches the analysis of the oscillations of prices of financial assets. This necessity leads to an argument about new alternatives in the prediction of financial time series using machine learning methods. Several models have been developed to perform the analysis and prediction of financial asset data. This thesis aims to propose the development of SVR-wavelet model, an adaptive and hybrid prediction model, which integrates wavelet models and Support Vector Regression (SVR), for prediction of Financial Time Series, particularly Foreign Exchange Market (FOREX), obtained from a public knowledge base. The method consists of using the Discrete Wavelets Transform (DWT) to decompose data from FOREX time series, that are used as SVR input variables to predict new data. The series are adjusted by generating new predictions of the original series, which are compared with other traditional models such as the Autoregressive Integrated Moving Average model (ARIMA), the Autoregressive Fractionally Integrated Moving Average model (ARFIMA), the Generalized Autoregressive Conditional Heteroskedasticity model (GARCH) and the traditional SVR model with Kernel. In addition, normality and unit root tests for non-linear distribution, and correlation tests, are performed to verify that the FOREX time series are adequate for the verification of SVR-wavelet hybrid model and comparison with traditional models. There is also the adherence to the Hurst Exponent through the statistical Rescaled Range (R/S).

Converging evidence from a variety of fields, including psychiatry, suggests that the temporal correlates of the brain’s resting state could serve as essential markers of a healthy and efficient brain. We use ketamine to induce schizophrenia-like states in 32 healthy individuals to examine the brain’s resting states using fMRI. We found a global reduction in temporal variability quantified by the time series’ standard deviation and an increase in scale-free properties quantified by the Hurst exponent representing the signal self-affinity over time. We also found network-specific and frequency-specific effects of ketamine on these temporal measures. Our results confirm prior studies in aging, sleep, anesthesia, and psychiatry suggesting that increased self-affinity and decreased temporal variability of the brain resting state could indicate a compromised and inefficient brain state. Our results expand our systemic view of the temporal structure of the brain and shed light on promising biomarkers in psychiatry

The aim of this graduation thesis is the descriptiton of R/S analysis and it's aplication on chosen time series of share prices and exchange rates. Some main models of financial time series will be mentioned in the second chapter. There will described basic linear models of stationary and non stationary time series and models of volatility. Then we will focus on the main theme of this thesis, R/S analysis. The algorithm of R/S analysis and the interpretation of the Hurst exponent will be described in the forth chapter. In the fifth chapter, the R/S analysis will by applied on real data sets. There will be two data sest of share prices of Telefónica O2 and Philip Morris and two data sets of exchange rates CZK/EUR and CZK/USD. The results will be interpreted and compared.

No description available.

No description available.

Human postural control is a complex process, but that is critical to understand in order to reduce the prevalence of occupational falls. Localized muscle fatigue (LMF), altered sensory input, and inter-individual differences (e.g. age and gender) have been shown to influence postural control, and numerous methods have been developed in order to quantify such effects. Recently, methods based on statistical mechanics have become popular, and when applied to center of pressure (COP) data, appear to provide new information regarding the postural control system. This study addresses in particular the stabilogram diffusion and Hurst exponent methods. An existing dataset was employed, in which sway during quiet stance was measured under different visual and surface compliance conditions, among both genders and different age groups, as well as before and after induction of localized muscle fatigue at the ankle, knee, torso, and shoulder. The stabilogram diffusion method determines both short-term and long-term diffusion coefficients, which correspond to open- and closed-loop control of posture, respectively. To do so, a "critical point" (or critical time interval) needs to be determined to distinguish between the two diffusion regions. Several limitations are inherent in existing methods to determine this critical point. To address this, a new algorithm was developed, based on a wavelet transform of COP data. The new algorithm is able to detect local maxima over specified frequency bands within COP data; therefore it can identify postural control mechanisms correspondent to those frequency bands. Results showed that older adults had smaller critical time intervals, and indicating that sway control of older adults was essentially different from young adults. Diffusion coefficients show that among young adults, torso LMF significantly compromised sway stability. In contrast, older adults appeared more resistance to LMF. Similar to earlier work, vision was found to play a crucial role in maintaining sway stability, and that stability was worse under eyes-closed (EC) than eyes-opened (EO) conditions. It was also found that the short-term Hurst exponent was not successful at detecting the effects of LMF on sway stability, likely because of a small sample size. The new critical point identification algorithm was verified to have better sensitivity and reliability than the traditional approach. The new algorithm can be used in future work to aid in the assessment of postural control and the mechanisms underlying this control. / Master of Science

The main goal of this thesis is to test the ability of the Hurst exponent to recognise some processes with deterministic signal as nonrandom and to test the randomness of daily stock returns of three stocks traded in BCPP. Critical values to determine the critical region of a randomness hypothesis test were set for this purpose. Another goal of the thesis is the description of the Hurst exponent estimation by means of Rescaled Range Analysis and outline some problems accompanying this estimation if the Hurst exponent would be used as a randomness indicator. Within the frame of Rescaled Range Analysis was constructed another method that showed to be successful in recognising some series that contain deterministic signal.

Submitted by Angela Maria de Oliveira (amolivei@uepg.br) on 2018-11-22T18:11:23Z No. of bitstreams: 2 license_rdf: 811 bytes, checksum: e39d27027a6cc9cb039ad269a5db8e34 (MD5) Tiago Jacumasso.pdf: 9316680 bytes, checksum: 9e1e6195d90b660e6d32c4f13481bf5b (MD5) / Made available in DSpace on 2018-11-22T18:11:23Z (GMT). No. of bitstreams: 2 license_rdf: 811 bytes, checksum: e39d27027a6cc9cb039ad269a5db8e34 (MD5) Tiago Jacumasso.pdf: 9316680 bytes, checksum: 9e1e6195d90b660e6d32c4f13481bf5b (MD5) Previous issue date: 2018-08-31 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / A mecânica da fratura foi desenvolvida, utilizando-se uma descrição geométrica euclidiana que pressupõem uma trinca lisa sem irregularidades. Por esta razão, a modelagem matemática de uma trinca rugosa, usando a geometria fractal, tem sido a preocupação de vários autores nas últimas décadas. O intuito destes pesquisadores é descrever o fenômeno da fratura de forma mais autentica e precisa. Uma das formas de se avaliar as propriedades mecânicas de um material fraturado é usando o conceito de integral-J. Este conceito aplicado ao fenômeno da fratura define uma curva de resistência ao crescimento de trinca chamado de curva J-R. Sendo assim, vários modelos fractais de curva J-R têm sido propostos. Um dos modelos que vem ganhando destaque na literatura científica foi proposto por ALVES (2010, 2011). Por esta razão investigou-se, neste trabalho, a aplicação desse modelo no estudo da fratura do ferro fundido nodular e ferro fundido nodular austemperado (ADI). O objetivo foi avaliar os efeitos dos tratamentos térmicos de austêmpera na microestrutura e nas propriedades mecânicas de uma liga de ferro fundido nodular. Para tanto foi empregado duas rotas de tratamentos térmicos: austêmpera convencional, consistindo de austenitização a 900ºC por 60min, seguida de austêmpera até 250ºC e à 300ºC, com permanência por 60min e 120min para cada temperatura, totalizando quatro condições, com resfriamento ao ar. As amostras tratadas termicamente foram caracterizadas com auxílio de microscopia óptica, microscopia eletrônica de varredura (FEG) e difração de raios X (DRX), com objetivo de determinar suas fases e microconstituintes. O efeito das condições de tratamento nas propriedades mecânicas foi verificado por ensaios de dureza Vickers e de impacto instrumentado Charpy. Por meio de ensaios de impacto instrumentado e solicitação mecânica de tração e com o auxílio de microscopia eletrônica por emissão de campo (FEG) foi possível estudar o crescimento de trincas rugosas na fratura do ferro fundido nodular austemperado, comparando os resultados entre as quatro condições de tratamento térmico de austêmpera. Deste modo, foi possível fornecer dados experimentais para comprovar a validade da equação da curva J-R na presença de uma trinca rugosa proposta por ALVES (2010, 2011) com base na geometria fractal e na mecânica da fratura. Os resultados obtidos permitiram comparar e discutir o efeito das rotas de tratamento térmico, no sentido de desenvolver as propriedades mecânicas do ferro fundido nodular para aplicações diversas. As curvas D J ajustadas pelo modelo fractal mostraram-se em boa concordância com aquelas obtidas pelo método descrito na ASTM E1820-17a (2017). O ADI tratado a 300ºC por 60 minutos foi o material que apresentou as melhores condições de resistência mecânica a tração e ao impacto, superando o material bruto de fundição na tenacidade a fratura, calculada pelos parâmetros fractais da curva. Este ferro fundido nodular austemperado é comparado ao da classe de alta resistência de ADI. / The mechanics of the fracture were developed using a geometric Euclidean description that assumes a smooth crack without irregularities. For this reason, the mathematical modeling of a rough crack, using fractal geometry, has been the concern of several authors in the last decades. The aim of these researchers is to describe the fracture phenomenon more authentically and accurately. One of the ways to evaluate the mechanical properties of a fractured material is by using the concept of integral-J. This concept applied to the fracture phenomenon defines a crack growth resistance curve called the J-R curve. Thus, several fractal J-R curve models have been proposed. One of the models that have gained prominence in the scientific literature was proposed by ALVES (2010, 2011). For this reason we investigated the application of this model in the study of nodular cast iron and austempered nodular cast iron (ADI). The objective was to evaluate the effects of thermal treatments of austempering in the microstructure and mechanical properties of a ductile cast iron alloy. Two routes of thermal treatments were used: conventional austenitic, consisting of austenitization at 900ºC for 60min, followed by tempering up to 250ºC and at 300ºC, with permanence for 60min and 120min for each temperature, totaling four conditions, with air cooling. The thermally treated samples were characterized by optical microscopy, scanning electron microscopy (FEG) and X - ray diffraction (XRD), in order to determine their phases and microconstituents. The effect of the treatment conditions on the mechanical properties was verified by tests of Vickers hardness and instrumented impact Charpy. By means of instrumented impact and mechanical tensile stress tests and with the aid of field emission electron microscopy (FEG), it was possible to study the growth of rough cracks in austempered nodular cast iron fracture, comparing the results between the four conditions of heat treatment. Thus, it was possible to provide experimental data to prove the validity of the J-R curve equation in the presence of a rough crack proposed by ALVES (2010, 2011) based on fractal geometry and fracture mechanics. The results obtained allowed to compare and discuss the effect of heat treatment routes in order to develop the mechanical properties of nodular cast iron for different applications. The D J curves fitting by the fractal model show in agreement with the curves obtained by the method described in the ASTM E1820-17a (2017). The ADI treated at 300ºC for 60 minutes was the material that presented the best conditions of tensile and impact mechanical strength, surpassing the crude casting material in the fracture toughness, calculated by the fractal parameters of the curve. This austempered nodular cast iron is compared to that of the ADI high strength class.