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).

Traditional models of financial asset yields are based on a number of simplifying assumptions. Among these are the primary assumptions that changes in asset yields are independent, and that the distribution of these yields is approximately normal. The development of financial asset pricing models has also incorporated these assumptions. A general feature of the pricing models is that the relationship between the model variables is fundamentally linear. Recent empirical research has however identified the possibility for these relations to be non-linear. The empirical research focused primarily on methodological issues relating to the application of the classical rescaled adjusted range. Some of the major issues investigated were: the use of overlapping versus contiguous subseries lengths in the calculation of the statistic's Hurst exponent; the asymptotic distribution of the Hurst exponent for Gaussian time-series and long-term dependent fBm's; matters pertaining to the estimation of the expected rescaled adjusted range. Empirical research in this thesis also considered alternate applications of rescaled range analysis, other than modelling non-linear long-term dependence. Issues relating to the use of the technique for estimating long-term dependent ARFIMA processes, and some implications of long-term dependence for financial time-series have both been investigated. Overall, the general shape of the asymptotic distribution of the Hurst exponent has been shown to be invariant to the level of dependence in the underlying series. While the rescaled adjusted range is a biased indicator of the level of long-term dependence in simulated time-series, it was found that the bias could be efficiently modelled. For real time-series containing structured short-term dependence, the bias was shown to be inconsistent with the simulated results. / Doctor of Philosophy (PhD)

In this paper, we focus on the goodness of fit test for self-similar property of two well-known processes: the fractional Brownian motion and the fractional autoregressive integrated moving average process. The Hurst parameter of the self-similar process is estimated by the embedding branching process method proposed by Jones and Shen (2004). The goodness of fit test for self-similarity is based on the Pearson chi-square test statistic. We approximate the null distribution of the test statistic by a scaled chi-square distribution to correct the size bias problem of the conventional chi-square distribution. The scale parameter and degrees of freedom of the test statistic are determined via regression method. Simulations are performed to show the finite sample size and power of the proposed test. Empirical applications are conducted for the high frequency financial data and human heart rate data.

As applications like IPTV and VoD (Video on demand) are gaining popularity, it is becoming more important to study the behavior of video signals in the Internet access infrastructures such as ADSL and cable networks. Average delay, average jitter and packet loss in these networks affect the quality of service, hence transmission and access speeds need to be determined such that these parameters are minimized. In this study the behavior of the above mentioned IP networks under variable bit rate (VBR) video traffic is investigated. ns-2 simulator is used for this purpose and actual as well as artificially generated signals are applied to the networks under test. Variable bit rate (VBR) traffic is generated synthetically using ON/OFF sources with ON/OFF times taken from exponential or Pareto distributions. As VBR video shows long range dependence with a Hurst parameter between 0.5 and 1, this parameter was used as a metric to measure the accuracy of the synthetic sources. Two different topologies were simulated in this study: one similar to ADSL access networks and the other behaving like cable distribution network. The performance of the networks (delay, jitter and packet loss) under VBR video traffic and different access speeds were measured. According to the obtained results, minimum access speeds in order achieve acceptable quality video delivery to the customers were suggested.

Traditional financial modeling is based on semimartingale processes with stationary and independent increments. However, empirical investigations on financial data does not always support these assumptions. This contradiction showed that there is a need for new stochastic models. Fractional Brownian motion (fBm) was proposed as one of these models by Benoit Mandelbrot. FBm is the only continuous Gaussian process with dependent increments. Correlation between increments of a fBm changes according to its self-similarity parameter H. This property of fBm helps to capture the correlation dynamics of the data and consequently obtain better forecast results. But for values of H different than 1/2, fBm is not a semimartingale and classical Ito formula does not exist in that case. This gives rise to need for using the white noise theory to construct integrals with respect to fBm and obtain fractional Ito formulas. In this thesis, the representation of fBm and its fundamental properties are examined. Construction of Wick-Ito-Skorohod (WIS) and fractional WIS integrals are investigated. An Ito type formula and Girsanov type theorems are stated. The financial applications of fBm are mentioned and the Black&amp / Scholes price of a European call option on an asset which is assumed to follow a geometric fBm is derived. The statistical aspects of fBm are investigated. Estimators for the self-similarity parameter H and simulation methods of fBm are summarized. Using the R/S methodology of Hurst, the estimations of the parameter H are obtained and these values are used to evaluate the fractional Black&amp / Scholes prices of a European call option with different maturities. Afterwards, these values are compared to Black&amp / Scholes price of the same option to demonstrate the effect of long-range dependence on the option prices. Also, estimations of H at different time scales are obtained to investigate the multiscaling in financial data. An outlook of the future work is given.

Abstract The impenetrable movement and crash of the stock market is always the most intriguing research task of any financial researcher. Nowadays, it has been proved that the movements of financial asset have the property of non-linearity or near-chaos and shows some tendency within a given period. We used the R/S analysis as the tool to indicate the tendency, and those stocks as our researching objects. We then combined purely price technical analysis indicators and genetic algorithms to form a predicting model. Then we compared our genetic predicting model with the traditional ARIMA analysis and hope to find out the invisible pattern under price volatility. And we hope our model could assist investors in assessing the stock markets more objectively and reduce the risk of stock investment. The researching target is TSMC(2330). We covered the period from 5 September 1994 to 28 December 1999, resulting in 1490 trading days. Historical data are available from Taiwan Economic Journal (TEJ). We execute the researching comparison by bear-market, bull-market, and bull-then-bear market and concluded as follows. 1. After the R/S analysis, we got the Hurst exponent of TSMC to be 0.849855 and the trending cycle was 940. It has proved that the market has tendency and indirectly showed that the Taiwan stock market was not efficient. 2. According to directional precision, our predicting model apparently outpaced the ARIMA model in these three periods. The reason was that our model grabbed more information than the ARIMA model. 3. If we only think about the inputs and outputs, our model seems to be a proper framework for explaining the relationships among variables in comparison with the neural network model having the same input and output variables. 4. We can deduce the invisible relationships of price technical indicators and the closing price. 5. Genetic predicting model can detect the prevailing trend of the learning periods. 6. The shorter the learning period, the better the predicting effects. As a whole and conservatively speaking, we have 70% confidence in directional precision. 7. If we combine proper trading strategy with genetic predicting model and deduct the transaction cost, we still get a better profit than buy-and-hold strategy and have some maneuvering flexibility. 8. After hypothesis testing, our predicting model seems to have some potential of ex ante prediction, but the stability and usability still need further study. In short, we proposed the ex post stock price movement learning model and the viable direction of ex ante prediction. Investors can take advantage of the flexibility of the predicting model and avoid using the over-complex and rigid trading strategies.

Thesis (M.A.)--Villanova University, 2007. / English Dept. Includes bibliographical references.

Thesis (D. Min.)--Abilene Christian University, 1993. / Includes abstract. Includes bibliographical references (leaves 142-147).

Thesis (M.A.)--Villanova University, 2007. / English Department. Includes bibliographical references.

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.