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Mazviona, Batsirai Winmore. "Volatility forecasting using Double-Markov switching GARCH models under skewed Student-t distribution." Master's thesis, University of Cape Town, 2012. http://hdl.handle.net/11427/12344.
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Includes bibliographical references.<br>This thesis focuses on forecasting the volatility of daily returns using a double Markov switching GARCH model with a skewed Student-t error distribution. The model was applied to individual shares obtained from the Johannesburg Stock Exchange (JSE). The Bayesian approach which uses Markov Chain Monte Carlo was used to estimate the unknown parameters in the model. The double Markov switching GARCH model was compared to a GARCH(1,1) model. Value at risk thresholds and violations ratios were computed leading to the ranking of the GARCH and double Markov switching GARCH models. The results showed that double Markov switching GARCH model performs similarly to the GARCH model based on the ranking technique employed in this thesis.
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Busato, Erick Andrade. "Função de acoplamento t-Student assimetrica : modelagem de dependencia assimetrica." [s.n.], 2008. http://repositorio.unicamp.br/jspui/handle/REPOSIP/305857.
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Previous issue date: 2008<br>Resumo: A família de distribuições t-Student Assimétrica, construída a partir da mistura em média e variância da distribuição normal multivariada com a distribuição Inversa Gama possui propriedades desejáveis de flexibilidade para as mais diversas formas de assimetria. Essas propriedades são exploradas na construção de funções de acoplamento que possuem dependência assimétrica. Neste trabalho são estudadas as características e propriedades da distribuição t-Student Assimétrica e a construção da respectiva função de acoplamento, fazendo-se uma apresentação de diferentes estruturas de dependência que pode originar, incluindo assimetrias da dependência nas caudas. São apresentados métodos de estimação de parâmetros das funções de acoplamento, com aplicações até a terceira dimensão da cópula. Essa função de acoplamento é utilizada para compor um modelo ARMA-GARCHCópula com marginais de distribuição t-Student Assimétrica, que será ajustado para os logretornos de preços do Petróleo e da Gasolina, e log-retornos do Índice de Óleo AMEX, buscando o melhor ajuste, principalmente, para a dependência nas caudas das distribuições de preços. Esse modelo será comparado, através de medidas de Valor em Risco e AIC, além de outras medidas de bondade de ajuste, com o modelo de Função de Acoplamento t-Student Simétrico.<br>Abstract: The Skewed t-Student distribution family, constructed upon the multivariate normal mixture distribution, known as mean-variance mixture, composed with the Inverse-Gamma distribution, has many desirable flexibility properties for many distribution asymmetry structures. These properties are explored by constructing copula functions with asymmetric dependence. In this work the properties and characteristics of the Skewed t-Student distribution and the construction of a respective copula function are studied, presenting different dependence structures that the copula function generates, including tail dependence asymmetry. Parameter estimation methods are presented for the copula, with applications up to the 3rd dimension. This copula function is used to compose an ARMAGARCH- Copula model with Skewed t-Student marginal distribution that is adjusted to logreturns of Petroleum and Gasoline prices and log-returns of the AMEX Oil Index, emphasizing the return's tail distribution. The model will be compared, by the means of the VaR (Value at Risk) and Akaike's Information Criterion, along with other Goodness-of-fit measures, with models based on the Symmetric t-Student Copula.<br>Mestrado<br>Mestre em Estatística
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Ali, Mohamed Khadar. "Applying Value at Risk (VaR) analysis to Brent Blend Oil prices." Thesis, Högskolan i Gävle, Avdelningen för ekonomi, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:hig:diva-10798.
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The purpose with this study is to compare four different models to VaR in terms of accuracy, namely Historical Simulation (HS), Simple Moving Average (SMA), Exponentially Weighted Moving Average (EWMA) and Exponentially Weighted Historical Simulation (EWHS). These VaR models will be applied to one underlying asset which is the Brent Blend Oil using these confidence levels 95 %, 99 % and 99, 9 %. Concerning the return of the asset the models under two different assumptions namely student t-distribution and normal distribution will be studied
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Percy, Edward Richard Jr. "Corrected LM goodness-of-fit tests with applicaton to stock returns." The Ohio State University, 2006. http://rave.ohiolink.edu/etdc/view?acc_num=osu1134416514.
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Ozturk, Kevser. "Exchange Rate Volatility: The Case Of Turkey." Master's thesis, METU, 2006. http://etd.lib.metu.edu.tr/upload/12608026/index.pdf.
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In this study, different from previous studies, the explanatory power of Student-t distribution is compared to normal distribution by employing both standard GARCH and EGARCH models to dollar/ lira (USD/TRY) exchange rate. Then the impact of Central Bank of Republic of the Turkey&rsquo<br>s (CBRT) decisions and actions on both the level of exchange rate and the volatility is investigated. Moreover the relationship between volatility and market liquidity is examined using spot foreign exchange (FX) market volume as a proxy. The results reveal that, in contrast to preceding findings, Student-t could not capture the leptokurtic property better than normal distribution does. Furthermore, an increase in Turkish government benchmark bond rates, CBRT FX purchase interventions and announcement of suspending/ decreasing-the-amount-of FX auctions lead Turkish lira to depreciate. Because of the significant positive leverage effect, the results of GARCH and EGARCH variance equations differ so much. Thereby the results should be evaluated cautiously. In addition it is observed that, only EGARCH model gives significant results when the spot market trading volume is included in the models
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Ofe, Hosea, and Peter Okah. "Value at Risk: A Standard Tool in Measuring Risk : A Quantitative Study on Stock Portfolio." Thesis, Umeå universitet, Handelshögskolan vid Umeå universitet, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-45303.
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The role of risk management has gained momentum in recent years most notably after the recent financial crisis. This thesis uses a quantitative approach to evaluate the theory of value at risk which is considered a benchmark to measure financial risk. The thesis makes use of both parametric and non parametric approaches to evaluate the effectiveness of VAR as a standard tool in measuring risk of stock portfolio. This study uses the normal distribution, student t-distribution, historical simulation and the exponential weighted moving average at 95% and 99% confidence levels on the stock returns of Sonny Ericsson, Three Months Swedish Treasury bill (STB3M) and Nordea Bank. The evaluations of the VAR models are based on the Kupiec (1995) Test. From a general perspective, the results of the study indicate that VAR as a proxy of risk measurement has some imprecision in its estimates. However, this imprecision is not all the same for all the approaches. The results indicate that models which assume normality of return distribution display poor performance at both confidence levels than models which assume fatter tails or have leptokurtic characteristics. Another finding from the study which may be interesting is the fact that during the period of high volatility such as the financial crisis of 2008, the imprecision of VAR estimates increases. For the parametric approaches, the t-distribution VAR estimates were accurate at 95% confidence level, while normal distribution approach produced inaccurate estimates at 95% confidence level. However both approaches were unable to provide accurate estimates at 99% confidence level. For the non parametric approaches the exponentially weighted moving average outperformed the historical simulation approach at 95% confidence level, while at the 99% confidence level both approaches tend to perform equally. The results of this study thus question the reliability on VAR as a standard tool in measuring risk on stock portfolio. It also suggest that more research should be done to improve on the accuracy of VAR approaches, given that the role of risk management in today’s business environment is increasing ever than before. The study suggest VAR should be complemented with other risk measures such as Extreme value theory and stress testing, and that more than one back testing techniques should be used to test the accuracy of VAR.
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Ashurbekova, Karina. "High-dimensional robust structure learning." Thesis, Université Grenoble Alpes (ComUE), 2019. http://www.theses.fr/2019GREAT100.
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L'apprentisage de structure de graphes est un problème essentiel dans de nombreuses applications, i.e. génétiques, neuroscience.L'estimation de la matrice de covariance/précision est le point crucial. Les techniques usuelles souffrent de deux problèmes. Le premier problème est la robustesse aux données non gaussiennes. Le second problème est le manque de données quand le nombre de paramètres à estimer est trop grand devant la taille de l'échantillon disponible. L'objectif de cette thèse est de fournir des méthodes robustes et adaptée à une faible taille d'échantillon.La première contribution de cette thèse considère les estimateurs de maximum de vraisemblance de la matrice de covariance avec shrinkage sous l'hypothèse de distributions à queue lourde et moyenne inconnue. La difficulté principale est le choix du paramètre de régularisation. Nous dérivons une expression explicite du coefficient de shrinkage pour toute distribution elliptique. Nous proposons aussi un algorithm dans le cas de distribution de Student multivariée qui est appliqué à des données simulées et des données réelles.La deuxième contribution concerne l'estimation de matrice de précision parcimonieuse pour des données non gaussiennes. En partant des résultats de la littérature, nous avons généralisé ceux-ci à des modèles de mélanges en grande dimension pour une sous-classe de famille de distribution elliptique.Pour finir, nous avons testé nos approches sur des données réelles d'IRMf. La structure estimée est soit la correlation soit la correlation partielle. Nous proposons une nouvelle construction de graphes prenant en compte la correlation et la correlation partielle. Cette nouvelle approche est validée sur des simulations et des données réelles<br>Structure learning in graphical models is an essential topic in different application areas, i.e., genetics, neuroscience. The crucial part of this model is the estimation of covariance/precision matrices. Traditional techniques for handling this problem suffer from two main issues. The first one is the lack of robustness when samples are assumed to follow a Gaussian distribution. The second one is the lack of data when the number of parameters to estimate is too large compared to the number of samples. Thus this thesis aims to build robust high-dimensional models for covariance and precision matrices estimation.The first question we address in the manuscript is the link between zero elements of precision matrices and the measure of the relationship between variables it reveals for different distributions.par In the first main contribution of this thesis we consider the shrinked likelihood-based estimators of the covariance matrix under the assumption of heavy-tailed distribution with unknown mean vector. The main difficulty at this point is the choice of the regularization parameters. We provide a closed-form expression of an optimal shrinkage coefficient for any sample distribution in the elliptical family. Based on these results, an algorithm for the case of the multivariate t-distribution with the simulated and real data is presented.The second contribution is dealing with sparse precision matrix estimation for the non-Gaussian data. Starting with the traditional techniques, we are able to generalize results for the high-dimensional mixture models for the subclass of elliptical family.Finally, we test our graph structure learning approach on brain signals using fMRI. The structure induced by both the correlation and the partial correlation is considered. We then propose a new graph construction method taking into account both conditional and marginal independences. The proposed approach shows better results than classical algorithms
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Kim, Young Il. "Essays on Volatility Risk, Asset Returns and Consumption-Based Asset Pricing." The Ohio State University, 2008. http://rave.ohiolink.edu/etdc/view?acc_num=osu1211912340.
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Freire, Paulo Guilherme de Lima. "Segmentação de placas de esclerose múltipla em imagens de ressonância magnética usando modelos de mistura de distribuições t-Student e detecção de outliers." Universidade Federal de São Carlos, 2016. https://repositorio.ufscar.br/handle/ufscar/7736.
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Previous issue date: 2016-02-15<br>Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)<br>Multiple Sclerosis (MS) is an inflammatory demyelinating (that is, with myelin loss) disease of the Central Nervous System (CNS). It is considered an autoimmune disease in which the immune system wrongly recognizes the myelin sheath of the CNS as an external element and attacks it, resulting in inflammation and scarring (sclerosis) of multiple areas of CNS’s white matter. Multi-contrast magnetic resonance imaging (MRI) has been successfully used in diagnosing and monitoring MS due to its excellent properties such as high resolution and good differentiation between soft tissues. Nowadays, the preferred method to segment MS lesions is the manual segmentation, which is done by specialists with limited help of a computer. However, this approach is tiresome, expensive and prone to error due to inter- and intra-variability between observers caused by low contrast on lesion edges. The challenge in automatic detection and segmentation of MS lesions in MR images is related to the variability of size and location of lesions, low contrast due to partial volume effect and the high range of forms that lesions can take depending on the stage of the disease. Recently, many researchers have turned their efforts into developing techniques that aim to accurately measure volumes of brain tissues and MS lesions, and also to reduce the amount of time spent on image analysis. In this context, this project proposes the study and development of an automatic computational technique based on an outlier detection approach, Student’s
t-distribution finite mixture models and probabilistic atlases to segment and measure MS
lesions volumes in MR images.<br>Esclerose Múltipla (EM) é uma doença inflamatória e desmielinizante (isto é, com perda
de mielina) do sistema nervoso central (SNC). É considerada uma doença autoimune a
qual o sistema imunológico reconhece erroneamente a bainha de mielina do SNC como
um elemento externo e então a ataca, resultando em inflamação e formação de cicatrizes
gliais (escleroses) em múltiplas áreas da substância branca do SNC. O imageamento multi-
contraste por ressonância magnética (RM) tem sido usado clinicamente com muito sucesso
para o diagnóstico e monitoramento da EM devido às suas excelentes propriedades como
alta resolução e boa diferenciação de tecidos moles. Atualmente, o método utilizado para
a segmentação de lesões de EM é o delineamento manual em imagens 3D de RM, o qual é
realizado por especialistas com ajuda limitada do computador. Entretanto, tal procedimento
é custoso e propenso à variabilidade inter e intraobservadores devido ao baixo contraste das
bordas das lesões. A grande dificuldade na detecção e segmentação automáticas das le-
sões de EM em imagens de RM está associada às suas variações no tamanho e localização,
baixo contraste decorrente do efeito de volume parcial e o amplo espectro de aparências
(realçadas, não-realçadas, black-holes) que elas podem ter, dependendo do estado evolutivo
da doença. Atualmente, vários pesquisadores têm voltado seus esforços para o desenvol-
vimento de técnicas que visam diminuir o tempo gasto na análise das imagens e medir, de
maneira mais precisa, o volume dos tecidos cerebrais e das lesões de EM. Nesse contexto,
este projeto propõe o estudo e o desenvolvimento de uma técnica computacional automá-
tica, baseada na abordagem de detecção de outliers e usando modelos de misturas finitas de
distribuições t-Student e atlas probabilísticos para a segmentação e medição do volume de
lesões de EM em imagens de RM.<br>FAPESP: 2014/00019-6
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Blad, Wiktor, and Vilim Nedic. "GARCH models applied on Swedish Stock Exchange Indices." Thesis, Uppsala universitet, Statistiska institutionen, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-386185.
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In the financial industry, it has been increasingly popular to measure risk. One of the most common quantitative measures for assessing risk is Value-at-Risk (VaR). VaR helps to measure extreme risks that an investor is exposed to. In addition to acquiring information of the expected loss, VaR was introduced in the regulatory frameworks of Basel I and II as a standardized measure of market risk. Due to necessity of measuring VaR accurately, this thesis aims to be a contribution to the research field of applying GARCH-models to financial time series in order to forecast the conditional variance and find accurate VaR-estimations. The findings in this thesis is that GARCH-models which incorporate the asymmetric effect of positive and negative returns perform better than a standard GARCH. Further on, leptokurtic distributions have been found to outperform normal distribution. In addition to various models and distributions, various rolling windows have been used to examine how the forecasts differ given window lengths.
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Heracleous, Maria S. "Volatility Modeling Using the Student's t Distribution." Diss., Virginia Tech, 2003. http://hdl.handle.net/10919/29126.
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Over the last twenty years or so the Dynamic Volatility literature has produced a wealth of univariate and multivariate GARCH type models. While the univariate models have been relatively successful in empirical studies, they suffer from a number ofweaknesses, such as unverifiable parameter restrictions, existence of moment conditions and the retention of Normality. These problems are naturally more acute in the multivariate GARCH type models, which in addition have the problem of overparameterization.
This dissertation uses the Student's t distribution and follows the Probabilistic Reduction (PR) methodology to modify and extend the univariate and multivariate volatility models viewed as alternative to the GARCH models. Its most important advantage is that it gives rise to internally consistent statistical models that do not require ad hoc parameter restrictions unlike the GARCH formulations.
Chapters 1 and 2 provide an overview of my dissertation and recent developments in the volatility literature. In Chapter 3 we provide an empirical illustration of the PR approach for modeling univariate volatility. Estimation results suggest that the Student's t AR model is a parsimonious and statistically adequate representation of exchange rate returns and Dow Jones returns data. Econometric modeling based on the Student's t distribution introduces an additional variable - the degree of freedom parameter. In Chapter 4 we focus on two questions relating to the `degree of freedom' parameter. A simulation study is used to examine:(i) the ability of the kurtosis coefficient to accurately capture the implied degrees of freedom, and (ii) the ability of Student's t GARCH model to estimate the true degree of freedom parameter accurately. Simulation results reveal that the kurtosis coefficient and the Student's t GARCH model (Bollerslev, 1987) provide biased and inconsistent estimators of the degree of freedom parameter.
Chapter 5 develops the Students' t Dynamic Linear Regression (DLR) }model which allows us to explain univariate volatility in terms of: (i) volatility in the past history of the series itself and (ii) volatility in other relevant exogenous variables. Empirical results of this chapter suggest that the Student's t DLR model provides a promising way to model volatility. The main advantage of this model is that it is defined in terms of observable random variables and their lags, and not the errors as is the case with the GARCH models. This makes the inclusion of relevant exogenous variables a natural part of the model set up.
In Chapter 6 we propose the Student's t VAR model which deals effectively with several key issues raised in the multivariate volatility literature. In particular, it ensures positive definiteness of the variance-covariance matrix without requiring any unrealistic coefficient restrictions and provides a parsimonious description of the conditional variance-covariance matrix by jointly modeling the conditional mean and variance functions.<br>Ph. D.
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Rahman, Azizur. "Bayesian prediction distributions for some linear models under student-t errors." University of Southern Queensland, Faculty of Sciences, 2007. http://eprints.usq.edu.au/archive/00003581/.
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[Abstract]: This thesis investigates the prediction distributions of future response(s), conditional on a set of realized responses for some linear models havingstudent-t error distributions by the Bayesian approach under the uniform priors. The models considered in the thesis are the multiple regression modelwith multivariate-t errors and the multivariate simple as well as multiple re-gression models with matrix-T errors. For the multiple regression model, results reveal that the prediction distribution of a single future response anda set of future responses are a univariate and multivariate Student-t distributions respectively with appropriate location, scale and shape parameters.The shape parameter of these prediction distributions depend on the size of the realized responses vector and the dimension of the regression parameters' vector, but do not depend on the degrees of freedom of the error distribu-tion. In the multivariate case, the distribution of a future responses matrix from the future model, conditional on observed responses matrix from the realized model for both the multivariate simple and multiple regression mod-els is matrix-T distribution with appropriate location matrix, scale factors and shape parameter. The results for both of these models indicate that prediction distributions depend on the realized responses only through the sample regression matrix and the sample residual sum of squares and products matrix. The prediction distribution also depends on the design matricesof the realized as well as future models. The shape parameter of the prediction distribution of the future responses matrix depends on size of the realized sample and the number of regression parameters of the multivariatemodel. Furthermore, the prediction distributions are derived by the Bayesian method as multivariate-t and matrix-T are identical to those obtained under normal errors' distribution by the di®erent statistical methods such as the classical, structural distribution and structural relations of the model approaches. This indicates not only the inference robustness with respect todepartures from normal error to Student-t error distributions, but also indicates that the Bayesian approach with a uniform prior is competitive withother statistical methods in the derivation of prediction distribution.
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Oger, Julie. "Méthodes probabilistes pour l'évaluation de risques en production industrielle." Phd thesis, Université François Rabelais - Tours, 2014. http://tel.archives-ouvertes.fr/tel-00982740.
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Dans un contexte industriel compétitif, une prévision fiable du rendement est une information primordiale pour déterminer avec précision les coûts de production et donc assurer la rentabilité d'un projet. La quantification des risques en amont du démarrage d'un processus de fabrication permet des prises de décision efficaces. Durant la phase de conception d'un produit, les efforts de développement peuvent être alors identifiés et ordonnés par priorité. Afin de mesurer l'impact des fluctuations des procédés industriels sur les performances d'un produit donné, la construction de la probabilité du risque défaillance est développée dans cette thèse. La relation complexe entre le processus de fabrication et le produit conçu (non linéaire, caractéristiques multi-modales...) est assurée par une méthode de régression bayésienne. Un champ aléatoire représente ainsi, pour chaque configuration du produit, l'information disponible concernant la probabilité de défaillance. Après une présentation du modèle gaussien, nous décrivons un raisonnement bayésien évitant le choix a priori des paramètres de position et d'échelle. Dans notre modèle, le mélange gaussien a priori, conditionné par des données mesurées (ou calculées), conduit à un posterior caractérisé par une distribution de Student multivariée. La nature probabiliste du modèle est alors exploitée pour construire une probabilité de risque de défaillance, définie comme une variable aléatoire. Pour ce faire, notre approche consiste à considérer comme aléatoire toutes les données inconnues, inaccessibles ou fluctuantes. Afin de propager les incertitudes, une approche basée sur les ensembles flous fournit un cadre approprié pour la mise en oeuvre d'un modèle bayésien imitant le raisonnement d'expert. L'idée sous-jacente est d'ajouter un minimum d'information a priori dans le modèle du risque de défaillance. Notre méthodologie a été mise en oeuvre dans un logiciel nommé GoNoGo. La pertinence de cette approche est illustrée par des exemples théoriques ainsi que sur un exemple réel provenant de la société STMicroelectronics.
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Roth, Michael, Emre Ozkan, and Fredrik Gustafsson. "A student's t filter for heavy tailed process and measurement noise." Linköpings universitet, Reglerteknik, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-93704.
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We consider the filtering problem in linear state space models with heavy tailed process and measurement noise. Our work is based on Student's t distribution, for which we give a number of useful results. The derived filtering algorithm is a generalization of the ubiquitous Kalman filter, and reduces to it as special case. Both Kalman filter and the new algorithm are compared on a challenging tracking example where a maneuvering target is observed in clutter.<br>MC Impulse
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Dodgson, J. H. "The effect of a preliminary test of normality using √b₁ on Student's t Distribution." Thesis, Loughborough University, 1987. https://dspace.lboro.ac.uk/2134/32331.
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Student's t Distribution is introduced with background including comments on its robustness properties. The ad hoc procedure of pretesting data for normality is discussed in the light of current advice, and previous work into its effectiveness reviewed. The approach to the problem is outlined: √b1 for test statistic, the Gram-Charlier distribution for population, approximations using the Johnson system.
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Kastner, Gregor. "Heavy-Tailed Innovations in the R Package stochvol." WU Vienna University of Economics and Business, 2015. http://epub.wu.ac.at/4918/1/heavytails.pdf.
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We document how sampling from a conditional Student's t distribution is implemented in stochvol. Moreover, a simple example using EUR/CHF exchange rates illustrates how to use the augmented sampler. We conclude with results and implications. (author's abstract)
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Hou, Zhijie. "On modeling the volatility in speculative prices." Diss., Virginia Tech, 2014. http://hdl.handle.net/10919/48925.
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Following the Probabilistic Reduction(PR) Approach, this paper proposes the Student’s Autoregressive (St-AR) Model, Student’s t Vector Autoregressive (St-VAR) Model and their heterogeneous versions, as an alternative to the various ARCH type models, to capture univariate and multivariate volatility. The St-AR and St-VAR models differ from the latter volatility models because they give rise to internally consistent statistical models that do not rely on ad-hoc specification and parameter restrictions, but model the conditional mean and conditional variance jointly.
The univariate modeling is illustrated using the Real Effect Exchange Rate(REER) indices of three mainstream currencies in Asia (RMB, Hong Kong Dollar and Taiwan Dollar), while the multivariate volatility modeling is applied to investigate the relationship between the REER indices and stock price indices in mainland China, as well as the relationship between the stock prices in mainland China and Hong Kong. Following the PR methodology, the information gained in Mis-Specification(M-S) testing leads to respecification strategies from the original Normal-(V)AR models to the St-(V)AR models. The results from formal Mis-Specification (M-S) tests and forecasting performance indicate that the St-(V)AR models provide a more appropriate way to model volatility for certain types of speculative price data.<br>Ph. D.
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Macerau, Walkiria Maria de Oliveira. "Comparação das distribuições α-estável, normal, t de student e Laplace assimétricas". Universidade Federal de São Carlos, 2012. https://repositorio.ufscar.br/handle/ufscar/4555.
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Previous issue date: 2012-01-27<br>Financiadora de Estudos e Projetos<br>Abstract The asymmetric distributions has experienced great development in recent times. They are used in modeling financial data, medical, genetics and other applications. Among these distributions, the Skew normal (Azzalini, 1985) has received more attention from researchers (Genton et al., (2001), Gupta et al., (2004) and Arellano-Valle et al., (2005)). We present a comparative study of _-stable distributions, Skew normal, Skew t de Student and Skew Laplace. The _-stable distribution is studied by Nolan (2009) and proposed by Gonzalez et al., (2009) in the context of genetic data. For some real datasets, in areas such as financial, genetics and commodities, we test which distribution best fits the data. We compare these distributions using the model selection criteria AIC and BIC.<br>As distribuições assimétricas tem experimentado grande desenvolvimento nos tempos recentes. Elas são utilizadas na modelagem de dados financeiros, médicos e genéticos entre outras aplicações. Dentre essas distribuições, a normal assimétrica (Azzalini, 1985) tem recebido mais atenção dos pesquisadores (Genton et al., (2001), Gupta et al., (2004) e Arellano-Valle et al., (2005)). Nesta dissertação, apresentamos um estudo comparativo das distribuições _-estável, normal , t de Student e Laplace assimétricas. A distribuição _-estável estudada por Nolan (2009) é proposta por Gonzalez et al., (2009) no contexto de dados genéticos. Neste trabalho, também apresentamos como verificar a assimetria de uma distribuição, descrevemos algumas características das distribuições assimétricas em estudo, e comparamos essas distribuições utilizando os critérios de seleção de modelos AIC e BIC..
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Lengua, Lafosse Patricia. "An empirical application of stochastic volatility models to Latin-American stock returns using GH skew student's t-distribution." Master's thesis, Pontificia Universidad Católica del Perú, 2015. http://tesis.pucp.edu.pe/repositorio/handle/123456789/6167.
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This paper represents empirical studies of stochastic volatility (SV) models for daily stocks returns data of a set of Latin American countries (Argentina, Brazil, Chile, Mexico and Peru) for the sample period 1996:01-2013:12. We estimate SV models incorporating both leverage effects and skewed heavy-tailed disturbances taking into account the GH Skew Student’s t-distribution using the Bayesian estimation method proposed by Nakajima and Omori (2012).
A model comparison between the competing SV models with symmetric Student´s t-disturbances is provided using the log marginal likelihoods in the empirical study. A prior sensitivity analysis is also provided. The results suggest that there are leverage effects in all indices considered but there is not enough evidence for Peru, and skewed heavy-tailed disturbances is confirmed only for Argentina, symmetric heavy-tailed disturbances for Mexico, Brazil and Chile, and symmetric Normal disturbances for Peru. Furthermore, we find that the GH Skew Student s t-disturbance distribution in the SV model is successful in describing the distribution of the daily stock return data for Peru, Argentina and Brazil over the traditional symmetric Student´s t-disturbance distribution.<br>Tesis
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Lengua, Lafosse Patricia, and Gabriel Rodríguez. "An empirical application of a stochastic volatility model with GH skew Student's t -distribution to the volatility of Latin-American stock returns." Elsevier B.V, 2018. http://hdl.handle.net/10757/624614.
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El texto completo de este trabajo no está disponible en el Repositorio Académico UPC por restricciones de la casa editorial donde ha sido publicado<br>Using daily stocks returns data of a set of Latin-American countries (Argentina, Brazil, Chile, Mexico and Peru) for the sample period 1996:01–2013:12, we estimate a stochastic volatility model incorporating both leverage effects and skewed heavy-tailed disturbances through of the GH Skew Student's t-distribution based on Bayesian estimation method proposed by Nakajima and Omori (2012). Two alternative models are estimated, one using an alternative Skew Student's t-distribution and the other using a symmetric Student's t-distribution. The results suggest the presence of leverage effects in all markets except for Peru where the evidence is unclear. In addition, there is evidence of asymmetries and heavy tails in the Argentina and S&P500 markets while in the other countries there is no robust evidence of such characteristics. Using the Bayes factor, the results indicate that the SVGHSkewt model dominates the other two models for the cases of Peru, Argentina, Brazil and S&P500 whereas the simple SVt model is preferred for the markets of Mexico and Chile. Similar findings are obtained after performing a robustness analysis regarding the priors of the parameters associated with the skewness and the tails of the distribution.<br>Revisión por pares
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Shen, Che. "An exploration of students' construction of meaning through symbolic manipulation and table/graph use in statistical inference tasks : the cases of normal and t distributions." Thesis, University of East Anglia, 2012. https://ueaeprints.uea.ac.uk/48142/.
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This study investigates college students’ use of statistics tables when solving problems on normal distribution and t distribution. Particular attention is given to the way in which students use the graphical representation of the normal curve and the t-curve in their solutions. A review of the literature on the teaching and learning of statistics at undergraduate level reveals that not much work has been carried out to investigate how students use statistics tables. The data in this study was collected in a business school at a private institute of technology in the south of Taiwan. Ten students in the second year of their course and their teacher participated in the study. The students were interviewed three times during the course of one semester. The data collected include field notes, audio recording and photos of classroom observation; participants’ answer sheet in the mid-term and final examinations, and exercise questions and audio/video recordings in the interviews. The main body of data are the clinical interviews carried out with the students. In these interviews the students were asked to solve statistics problems using a talk-aloud technique. The interviews were audio recorded and fully transcribed. The interview data were analysed by decomposing the students’ answer into the solving steps used in the solution of each problem. Analysis of the participants’ solutions revealed that using the tables of distribution to find the solution to the given task was problematic. Their solution attempts can be categorised into six types, but the underlying difficulty appeared to be the symbolic manipulation of the data in the question. Students seem not to ascribe statistics meaning to the symbols and tend to perform symbolic manipulations without investigating the meaning of the symbols first. Moreover, most participants did not use graphs when they solved the problems, and only four participants actively used graphs in a few questions, perhaps to visualise the values in the questions or to create meaning. The students who consistently used graphs in their solutions on the whole performed better than the ones who didn’t across the topics. The study concludes with some recommendations for the teaching of statistics as a service subject.
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Berberovic, Adnan, and Alexander Eriksson. "A Multi-Factor Stock Market Model with Regime-Switches, Student's T Margins, and Copula Dependencies." Thesis, Linköpings universitet, Produktionsekonomi, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-143715.
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Investors constantly seek information that provides an edge over the market. One of the conventional methods is to find factors which can predict asset returns. In this study we improve the Fama and French Five-Factor model with Regime-Switches, student's t distributions and copula dependencies. We also add price momentum as a sixth factor and add a one-day lag to the factors. The Regime-Switches are obtained from a Hidden Markov Model with conditional Student's t distributions. For the return process we use factor data as input, Student's t distributed residuals, and Student's t copula dependencies. To fit the copulas, we develop a novel approach based on the Expectation-Maximisation algorithm. The results are promising as the quantiles for most of the portfolios show a good fit to the theoretical quantiles. Using a sophisticated Stochastic Programming model, we back-test the predictive power over a 26 year period out-of-sample. Furthermore we analyse the performance of different factors during different market regimes.
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Börjesson, Carl, and Ossian Löhnn. "Univariate GARCH models with realized variance." Thesis, Uppsala universitet, Statistiska institutionen, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-386073.
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This essay investigates how realized variance affects the GARCH-models (GARCH, EGARCH, GJRGARCH) when added as an external regressor. The GARCH models are estimated with three different distributions; Normal-, Student’s t- and Normal inverse gaussian distribution. The results are ambiguous - the models with realized variance improves the model fit, but when applied to forecasting, the models with realized variance are performing similar Value at Risk predictions compared to the models without realized variance.
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Wallin, Edvin, and Timothy Chapman. "A heteroscedastic volatility model with Fama and French risk factors for portfolio returns in Japan." Thesis, Stockholms universitet, Statistiska institutionen, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-194779.
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This thesis has used the Fama and French five-factor model (FF5M) and proposed an alternative model. The proposed model is named the Fama and French five-factor heteroscedastic student's model (FF5HSM). The model utilises an ARMA model for the returns with the FF5M factors incorporated and a GARCH(1,1) model for the volatility. The FF5HSM uses returns data from the FF5M's portfolio construction for the Japanese stock market and the five risk factors. The portfolio's capture different levels of market capitalisation, and the factors capture market risk. The ARMA modelling is used to address the autocorrelation present in the data. To deal with the heteroscedasticity in daily returns of stocks, a GARCH(1,1) model has been used. The order of the GARCH-model has been concluded to be reasonable in academic literature for this type of data. Another finding in earlier research is that asset returns do not follow the assumption of normality that a regular regression model assumes. Therefore, the skewed student's t-distribution has been assumed for the error terms. The result of the data indicates that the FF5HSM has a better in-sample fit than the FF5M. The FF5HSM addresses heteroscedasticity and autocorrelation in the data and minimises them depending on the portfolio. Regardingforecasting, both the FF5HSM and the FF5M are accurate models depending on what portfolio the model is applied on.
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Jonsson, Fredrik. "Self-Normalized Sums and Directional Conclusions." Doctoral thesis, Uppsala universitet, Matematiska institutionen, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-162168.
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This thesis consists of a summary and five papers, dealing with self-normalized sums of independent, identically distributed random variables, and three-decision procedures for directional conclusions. In Paper I, we investigate a general set-up for Student's t-statistic. Finiteness of absolute moments is related to the corresponding degree of freedom, and relevant properties of the underlying distribution, assuming independent, identically distributed random variables. In Paper II, we investigate a certain kind of self-normalized sums. We show that the corresponding quadratic moments are greater than or equal to one, with equality if and only if the underlying distribution is symmetrically distributed around the origin. In Paper III, we study linear combinations of independent Rademacher random variables. A family of universal bounds on the corresponding tail probabilities is derived through the technique known as exponential tilting. Connections to self-normalized sums of symmetrically distributed random variables are given. In Paper IV, we consider a general formulation of three-decision procedures for directional conclusions. We introduce three kinds of optimality characterizations, and formulate corresponding sufficiency conditions. These conditions are applied to exponential families of distributions. In Paper V, we investigate the Benjamini-Hochberg procedure as a means of confirming a selection of statistical decisions on the basis of a corresponding set of generalized p-values. Assuming independence, we show that control is imposed on the expected average loss among confirmed decisions. Connections to directional conclusions are given.
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LIU, YI-WEI, та 劉宜緯. "α-Stable Distribution and its Application to Value at Risk and Financial Forecasting, in Comparison with Student''s t-Distribution". Thesis, 2015. http://ndltd.ncl.edu.tw/handle/p9tm6q.
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碩士<br>國立臺灣大學<br>財務金融學研究所<br>104<br>In practice, business people used to deal with financial data as if they follow the normal distribution. However, researches have shown that most financial assets returns possess fat-tailed property, which is contradictory to that of the normal distribution. Both the t-distribution and α-stable distribution are attractive alternatives. Past study have stated that the t-distribution dominates the normal distribution, but there is no definite dominance of either the t-distribution or the α-stable distribution over the other. They both carry unique features when fitted to financial data.
This paper compares the fitness of the t-distribution and the α-stable distribution to the stock indices returns in Asia, since most past researches of this kind focus on the equity indices in Europe and America. The analysis in this paper is classified into two parts, first the time independent part and followed by the time dependent part. In the first part, the Value at Risk (VaR) estimated by the unconditional t-distribution and the α-stable distribution are discussed. In the second part, the time series GARCH models with t-innovation and α-stable innovation respectively are also investigated.
The main finding is that in the sense of VaR, the unconditional α-stable distribution provides better estimates of VaR at moderate levels, and extreme VaR less than 1% with α-stable distribution tends to be conservative, with comparison to t-distribution. This is a valuable feature of the application of α-stable distribution to risk management, because it allows risk managers to preserve more reservation in advance for the potential upcoming losses.
Moreover, this paper also shows that the time series GARCH models with α-stable innovation always have smaller RMSE than those with t-innovation when the out-of-sample forecasting is conducted, indicating that the models with α-stable innovation may have better forecasting accuracy than those with t-innovation, though the degrees of significance are different due to the property of the data. Finally, the 95% forecasting intervals are constructed in this paper and they can be connected to the dynamic VaR, making it possible for us to estimate the VaR in accordance with time.
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Cao, Jian. "Computation of High-Dimensional Multivariate Normal and Student-t Probabilities Based on Matrix Compression Schemes." Diss., 2020. http://hdl.handle.net/10754/662613.
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The first half of the thesis focuses on the computation of high-dimensional multivariate normal (MVN) and multivariate Student-t (MVT) probabilities. Chapter 2 generalizes the bivariate conditioning method to a d-dimensional conditioning method and combines it with a hierarchical representation of the n × n covariance matrix. The resulting two-level hierarchical-block conditioning method requires Monte Carlo simulations to be performed only in d dimensions, with d ≪ n, and allows the dominant complexity term of the algorithm to be O(n log n). Chapter 3 improves the block reordering scheme from Chapter 2 and integrates it into the Quasi-Monte Carlo simulation under the tile-low-rank representation of the covariance matrix. Simulations up to dimension 65,536 suggest that this method can improve the run time by one order of magnitude compared with the hierarchical Monte Carlo method. The second half of the thesis discusses a novel matrix compression scheme with Kronecker products, an R package that implements the methods described in Chapter 3, and an application study with the probit Gaussian random field. Chapter 4 studies the potential of using the sum of Kronecker products (SKP) as a compressed covariance matrix representation. Experiments show that this new SKP representation can save the memory footprint by one order of magnitude compared with the hierarchical representation for covariance matrices from large grids and the Cholesky factorization in one million dimensions can be achieved within 600 seconds. In Chapter 5, an R package is introduced that implements the methods in Chapter 3 and show how the package improves the accuracy of the computed excursion sets. Chapter 6 derives the posterior properties of the probit Gaussian random field, based on which model selection and posterior prediction are performed. With the tlrmvnmvt package, the computation becomes feasible in tens of thousands of dimensions, where the prediction errors are significantly reduced.