Extreme Value Theory versus traditional GARCH approaches applied to financial data: a comparative evaluation

Although stock prices fluctuate, the variations are relatively small and are frequently assumed to be normal distributed on a large time scale. But sometimes these fluctuations can become determinant, especially when unforeseen large drops in asset prices are observed that could result in huge losses or even in market crashes. The evidence shows that these events happen far more often than would be expected under the generalized assumption of normal distributed financial returns. Thus it is crucial to properly model the distribution tails so as to be able to predict the frequency and magnitude of extreme stock price returns. In this paper we follow the approach suggested by McNeil and Frey (2000) and combine the GARCH-type models with the Extreme Value Theory (EVT) to estimate the tails of three financial index returns DJI,FTSE 100 and NIKKEI 225 representing three important financial areas in the world. Our results indicate that EVT-based conditional quantile estimates are much more accurate than those from conventional AR-GARCH models assuming normal or Student’s t-distribution innovations when doing out-of-sample estimation (within the insample estimation, this is so for the right tail of the distribution of returns).

The risk-return trade-off in Europe: A temporal and cross-sectional analysis

This paper analyzes the risk-return trade-off in European equities considering both temporal and cross-sectional dimensions. In our analysis, we introduce not only the market portfolio but also 15 industry portfolios comprising the entire market. Several bivariate GARCH models are estimated to obtain the covariance matrix between excess market returns and the industrial portfolios and the existence of a risk-return trade-off is analyzed through a cross-sectional approach using the information in all portfolios. It is obtained evidence for a positive and significant risk-return trade-off in the European market. This conclusion is robust for different GARCH specifications and is even more evident after controlling for the main financial crisis during the sample period.

Is stock market volatility persistent? A fractionally integrated approach

This paper seeks to study the persistence in the G7’s stock market volatility, which is carried out using the GARCH, IGARCH and FIGARCH models. The data set consists of the daily returns of the S&P/TSX 60, CAC 40, DAX 30, MIB 30, NIKKEI 225, FTSE 100 and S&P 500 indexes over the period 1999-2009. The results evidences long memory in volatility, which is more pronounced in Germany, Italy and France. On the other hand, Japan appears as the country where this phenomenon is less obvious; nevertheless, the persistence prevails but with minor intensity.

Volatility forecasting with range models: An evaluation of new alternatives to the CARR model

The aim of this paper is to analyze the forecasting ability of the CARR model proposed by Chou (2005) using the S&P 500. We extend the data sample, allowing for the analysis of different stock market circumstances and propose the use of various range estimators in order to analyze their forecasting performance. Our results show that there are two range-based models that outperform the forecasting ability of the GARCH model. The Parkinson model is better for upward trends and volatilities which are higher and lower than the mean while the CARR model is better for downward trends and mean volatilities.

Distribuição de sinais rádio e vídeo sobre fibra

As comunicações ópticas e as comunicações sem fios têm sofrido uma grande evolução ao longo das últimas décadas. Com o objectivo de juntar as vantagens de cada um dos sistemas surgiu o que se designa por rádio sobre fibra. Este sistema permite centralizar todo o processamento necessário num só local, na estação central, simplificando assim a estação base. Esta simplificação permite reduzir os custos de implementação e torna o sistema menos complexo. Esta dissertação de mestrado tem como objectivo principal estudar e simular um sistema que permite o envio de sinais vídeo e rádio pela fibra óptica para posterior difusão, utilizando o conceito de rádio sobre fibra. Os sinais enviados foram o LTE (Long Term Evolution), o UWB (Ultra WideBand) e o WiMAX (Worldwide Interoperability for Microwave Access). O primeiro disponibiliza o serviço de voz, o segundo disponibiliza o serviço de televisão e o último dá suporte à internet. Estes sinais foram modulados em OFDM (Orthogonal Frequency Division Multiplex), porque, posteriormente, estes sinais vão ser difundidos num ambiente sem fios e este tipo de modulação minimiza o efeito de multipercurso e da interferência intersimbólica. Com este estudo pretende-se verificar qual a viabilidade de um sistema que permite o envio de três sinais distintos simultaneamente (serviço Triple Play). Ao analisar os resultados deste sistema concluiu-se que a sua aplicabilidade pode apresentar algumas limitações, dependendo do tipo de modulação e do tipo de modulador que se utilize. Os moduladores ópticos utilizados foram o MZ (Mach-Zehnder) e o EA (Electro-Absorption). A qualidade do sinal recebido foi analisada com base no valor de EVM (Error Vector Magnitude). O primeiro modulador foi aquele que apresentou mais limitações, pois o desempenho do sistema é comprometido para distâncias superiores a 40 km e para potências de entrada inferiores a 0 dBm. Este tipo de sistema apresenta um EVM mais baixo quando a potência de entrada utilizada está entre 0 e 6 dBm. Se o modulador utilizado for o EA, o sistema apresenta um EVM mais baixo quando se utiliza um índice de modulação entre 20% e 30%, para uma potência de entrada entre 0 e 2 dBm.

Comunicações digitais através de ultra-sons em ambientes subaquáticos

Actualmente, as comunicações digitais em ambientes subaquáticos representam uma necessidade humana e um desafio à engenharia de sistemas. A maioria das aplicações dirigidas a meios subaquáticos recorre a sinais acústicos, já que relativamente a sinais de natureza electromagnética ou óptica, os sinais acústicos desfrutam de uma atenuação reduzida. Contudo, os meios subaquáticos possuem um comportamento complexo relativamente à propagação de sinais acústico, sendo caracterizados como canais dispersivos, no domínio do tempo e no domínio da frequência. Como os sistemas acústicos possuem uma largura de banda limitada, requer-se que um sistema de comunicação acústico subaquático seja, simultaneamente, eficiente na gestão dos recursos que possui e eficaz nos mecanismos que implementa para ultrapassar as limitações providenciadas pelo meio. Enquadrada neste âmbito, a presente dissertação propõe uma solução completa de um sistema de comunicação digital. Apresenta-se o dimensionamento de uma plataforma genérica, de baixo custo, que suporta a transmissão e recepção de sinais acústicos num ambiente subaquático. Através desta, verifica-se num meio subaquático real se as características deste ambiente coincidem com a informação presente na respectiva literatura científica. Adicionalmente, são analisadas quais as técnicas de processamento de sinal mais adequadas às comunicações digitais neste meio. Converge-se para uma solução baseada na modulação OFDM (Orthogonal Frequency Division Multiplexing), que alcança uma eficiência espectral de 2,95 bit/s/Hz, a um ritmo binário máximo de 103,288 kbit/s, numa largura de banda de 35 kHz. Através desta técnica, obtém-se elevada robustez aos efeitos de dispersão temporal do canal de comunicação, minimizando de forma eficaz a distorção de sinal devido à interferência inter-simbólica. Esta modulação multi-portadora recorre a sub-portadoras ortogonais, maximizando desta forma a eficiência espectral do sistema. Contudo, a ortogonalidade destas componentes pode ser comprometida pelo espalhamento de Doppler introduzido pelo canal subaquático. Para minimizar este efeito, é implementado um algoritmo adaptativo baseado na técnica LMS (Least Mean Squares).

Análise de clusters e volatilidade de índices de acções

Mestrado em Contabilidade e Gestão das Instituições Financeiras

Análise dos parâmetros de qualidade das imagens de verificação em radioterapia aplicada a patologias de cabeça e pescoço

Mestrado em Radiações Aplicadas às Tecnologias da Saúde - Área de especialização: Terapia com Radiações.

Implementação em hardware reconfigurável de método de separação de dados hiperespetrais

Relatório do Trabalho Final de Mestrado para obtenção do grau de Mestre em Engenharia de Electrónica e Telecomunicações

Implementação do protocolo eNAL num serviço de radioterapia: um estudo de caso

Mestrado em Radioterapia

Cluster de volatilidade no mercado de taxas de câmbio USD/GBP

Mestrado em Controlo de Gestão e dos Negócios

Assimetria na volatilidade dos principais índices bolsistas de Portugal, Irlanda, Itália, Grécia e Espanha : um estudo comparativo

Mestrado em Controlo de Gestão e dos Negócios

Crossing balanced and stair nested desings

Balanced nesting is the most usual form of nesting and originates, when used singly or with crossing of such sub-models, orthogonal models. In balanced nesting we are forced to divide repeatedly the plots and we have few degrees of freedom for the first levels. If we apply stair nesting we will have plots all of the same size rendering the designs easier to apply. The stair nested designs are a valid alternative for the balanced nested designs because we can work with fewer observations, the amount of information for the different factors is more evenly distributed and we obtain good results. The inference for models with balanced nesting is already well studied. For models with stair nesting it is easy to carry out inference because it is very similar to that for balanced nesting. Furthermore stair nested designs being unbalanced have an orthogonal structure. Other alternative to the balanced nesting is the staggered nesting that is the most popular unbalanced nested design which also has the advantage of requiring fewer observations. However staggered nested designs are not orthogonal, unlike the stair nested designs. In this work we start with the algebraic structure of the balanced, the stair and the staggered nested designs and we finish with the structure of the cross between balanced and stair nested designs.

Cobs and stair nesting – segregation and crossing

Stair nesting leads to very light models since the number of their treatments is additive on the numbers of observations in which only the level of one factor various. These groups of observations will be the steps of the design. In stair nested designs we work with fewer observations when compared with balanced nested designs and the amount of information for the different factors is more evenly distributed. We now integrate these models into a special class of models with orthogonal block structure for which there are interesting properties.

Unmixing hyperspectral data: independent and dependent component analysis

The development of high spatial resolution airborne and spaceborne sensors has improved the capability of ground-based data collection in the fields of agriculture, geography, geology, mineral identification, detection [2, 3], and classification [4–8]. The signal read by the sensor from a given spatial element of resolution and at a given spectral band is a mixing of components originated by the constituent substances, termed endmembers, located at that element of resolution. This chapter addresses hyperspectral unmixing, which is the decomposition of the pixel spectra into a collection of constituent spectra, or spectral signatures, and their corresponding fractional abundances indicating the proportion of each endmember present in the pixel [9, 10]. Depending on the mixing scales at each pixel, the observed mixture is either linear or nonlinear [11, 12]. The linear mixing model holds when the mixing scale is macroscopic [13]. The nonlinear model holds when the mixing scale is microscopic (i.e., intimate mixtures) [14, 15]. The linear model assumes negligible interaction among distinct endmembers [16, 17]. The nonlinear model assumes that incident solar radiation is scattered by the scene through multiple bounces involving several endmembers [18]. Under the linear mixing model and assuming that the number of endmembers and their spectral signatures are known, hyperspectral unmixing is a linear problem, which can be addressed, for example, under the maximum likelihood setup [19], the constrained least-squares approach [20], the spectral signature matching [21], the spectral angle mapper [22], and the subspace projection methods [20, 23, 24]. Orthogonal subspace projection [23] reduces the data dimensionality, suppresses undesired spectral signatures, and detects the presence of a spectral signature of interest. The basic concept is to project each pixel onto a subspace that is orthogonal to the undesired signatures. As shown in Settle [19], the orthogonal subspace projection technique is equivalent to the maximum likelihood estimator. This projection technique was extended by three unconstrained least-squares approaches [24] (signature space orthogonal projection, oblique subspace projection, target signature space orthogonal projection). Other works using maximum a posteriori probability (MAP) framework [25] and projection pursuit [26, 27] have also been applied to hyperspectral data. In most cases the number of endmembers and their signatures are not known. Independent component analysis (ICA) is an unsupervised source separation process that has been applied with success to blind source separation, to feature extraction, and to unsupervised recognition [28, 29]. ICA consists in finding a linear decomposition of observed data yielding statistically independent components. Given that hyperspectral data are, in given circumstances, linear mixtures, ICA comes to mind as a possible tool to unmix this class of data. In fact, the application of ICA to hyperspectral data has been proposed in reference 30, where endmember signatures are treated as sources and the mixing matrix is composed by the abundance fractions, and in references 9, 25, and 31–38, where sources are the abundance fractions of each endmember. In the first approach, we face two problems: (1) The number of samples are limited to the number of channels and (2) the process of pixel selection, playing the role of mixed sources, is not straightforward. In the second approach, ICA is based on the assumption of mutually independent sources, which is not the case of hyperspectral data, since the sum of the abundance fractions is constant, implying dependence among abundances. This dependence compromises ICA applicability to hyperspectral images. In addition, hyperspectral data are immersed in noise, which degrades the ICA performance. IFA [39] was introduced as a method for recovering independent hidden sources from their observed noisy mixtures. IFA implements two steps. First, source densities and noise covariance are estimated from the observed data by maximum likelihood. Second, sources are reconstructed by an optimal nonlinear estimator. Although IFA is a well-suited technique to unmix independent sources under noisy observations, the dependence among abundance fractions in hyperspectral imagery compromises, as in the ICA case, the IFA performance. Considering the linear mixing model, hyperspectral observations are in a simplex whose vertices correspond to the endmembers. Several approaches [40–43] have exploited this geometric feature of hyperspectral mixtures [42]. Minimum volume transform (MVT) algorithm [43] determines the simplex of minimum volume containing the data. The MVT-type approaches are complex from the computational point of view. Usually, these algorithms first find the convex hull defined by the observed data and then fit a minimum volume simplex to it. Aiming at a lower computational complexity, some algorithms such as the vertex component analysis (VCA) [44], the pixel purity index (PPI) [42], and the N-FINDR [45] still find the minimum volume simplex containing the data cloud, but they assume the presence in the data of at least one pure pixel of each endmember. This is a strong requisite that may not hold in some data sets. In any case, these algorithms find the set of most pure pixels in the data. Hyperspectral sensors collects spatial images over many narrow contiguous bands, yielding large amounts of data. For this reason, very often, the processing of hyperspectral data, included unmixing, is preceded by a dimensionality reduction step to reduce computational complexity and to improve the signal-to-noise ratio (SNR). Principal component analysis (PCA) [46], maximum noise fraction (MNF) [47], and singular value decomposition (SVD) [48] are three well-known projection techniques widely used in remote sensing in general and in unmixing in particular. The newly introduced method [49] exploits the structure of hyperspectral mixtures, namely the fact that spectral vectors are nonnegative. The computational complexity associated with these techniques is an obstacle to real-time implementations. To overcome this problem, band selection [50] and non-statistical [51] algorithms have been introduced. This chapter addresses hyperspectral data source dependence and its impact on ICA and IFA performances. The study consider simulated and real data and is based on mutual information minimization. Hyperspectral observations are described by a generative model. This model takes into account the degradation mechanisms normally found in hyperspectral applications—namely, signature variability [52–54], abundance constraints, topography modulation, and system noise. The computation of mutual information is based on fitting mixtures of Gaussians (MOG) to data. The MOG parameters (number of components, means, covariances, and weights) are inferred using the minimum description length (MDL) based algorithm [55]. We study the behavior of the mutual information as a function of the unmixing matrix. The conclusion is that the unmixing matrix minimizing the mutual information might be very far from the true one. Nevertheless, some abundance fractions might be well separated, mainly in the presence of strong signature variability, a large number of endmembers, and high SNR. We end this chapter by sketching a new methodology to blindly unmix hyperspectral data, where abundance fractions are modeled as a mixture of Dirichlet sources. This model enforces positivity and constant sum sources (full additivity) constraints. The mixing matrix is inferred by an expectation-maximization (EM)-type algorithm. This approach is in the vein of references 39 and 56, replacing independent sources represented by MOG with mixture of Dirichlet sources. Compared with the geometric-based approaches, the advantage of this model is that there is no need to have pure pixels in the observations. The chapter is organized as follows. Section 6.2 presents a spectral radiance model and formulates the spectral unmixing as a linear problem accounting for abundance constraints, signature variability, topography modulation, and system noise. Section 6.3 presents a brief resume of ICA and IFA algorithms. Section 6.4 illustrates the performance of IFA and of some well-known ICA algorithms with experimental data. Section 6.5 studies the ICA and IFA limitations in unmixing hyperspectral data. Section 6.6 presents results of ICA based on real data. Section 6.7 describes the new blind unmixing scheme and some illustrative examples. Section 6.8 concludes with some remarks.