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.

Does independent component analysis play a role in unmixing hyperspectral data?

Independent component analysis (ICA) has recently been proposed as a tool to unmix hyperspectral data. ICA is founded on two assumptions: 1) the observed spectrum vector is a linear mixture of the constituent spectra (endmember spectra) weighted by the correspondent abundance fractions (sources); 2)sources are statistically independent. Independent factor analysis (IFA) extends ICA to linear mixtures of independent sources immersed in noise. Concerning hyperspectral data, the first assumption is valid whenever the multiple scattering among the distinct constituent substances (endmembers) is negligible, and the surface is partitioned according to the fractional abundances. The second assumption, however, is violated, since the sum of abundance fractions associated to each pixel is constant due to physical constraints in the data acquisition process. Thus, sources cannot be statistically independent, this compromising the performance of ICA/IFA algorithms in hyperspectral unmixing. This paper studies the impact of hyperspectral source statistical dependence on ICA and IFA performances. We conclude that the accuracy of these methods tends to improve with the increase of the signature variability, of the number of endmembers, and of the signal-to-noise ratio. In any case, there are always endmembers incorrectly unmixed. We arrive to this conclusion by minimizing the mutual information of simulated and real hyperspectral mixtures. The computation of mutual information is based on fitting mixtures of Gaussians to the observed data. A method to sort ICA and IFA estimates in terms of the likelihood of being correctly unmixed is proposed.

Dependent component analysis: a hyperspectral unmixing algorithm

Linear unmixing decomposes a hyperspectral image into a collection of reflectance spectra of the materials present in the scene, called endmember signatures, and the corresponding abundance fractions at each pixel in a spatial area of interest. This paper introduces a new unmixing method, called Dependent Component Analysis (DECA), which overcomes the limitations of unmixing methods based on Independent Component Analysis (ICA) and on geometrical properties of hyperspectral data. DECA models the abundance fractions as mixtures of Dirichlet densities, thus enforcing the constraints on abundance fractions imposed by the acquisition process, namely non-negativity and constant sum. The mixing matrix is inferred by a generalized expectation-maximization (GEM) type algorithm. The performance of the method is illustrated using simulated and real data.

Does Independent Component Analysis Play a Role in Unmixing Hyperspectral Data?

Chapter in Book Proceedings with Peer Review First Iberian Conference, IbPRIA 2003, Puerto de Andratx, Mallorca, Spain, JUne 4-6, 2003. Proceedings

Parallel implementation of vertex component analysis for hyperspectral endmember extraction

International Conference with Peer Review 2012 IEEE International Conference in Geoscience and Remote Sensing Symposium (IGARSS), 22-27 July 2012, Munich, Germany

Pulmonary tuberculosis in Continental Portugal 2000-2010: temporal trends clustering as a tool for control evaluation

Clustering analysis is a useful tool to detect and monitor disease patterns and, consequently, to contribute for an effective population disease management. Portugal has the highest incidence of tuberculosis in the European Union (in 2012, 21.6 cases per 100.000 inhabitants), although it has been decreasing consistently. Two critical PTB (Pulmonary Tuberculosis) areas, metropolitan Oporto and metropolitan Lisbon regions, were previously identified through spatial and space-time clustering for PTB incidence rate and risk factors. Identifying clusters of temporal trends can further elucidate policy makers about municipalities showing a faster or a slower TB control improvement.

Optimizing the renewable generation mix in the Portuguese power system based on temporal and spatial diversity

Renewable energy sources (RES) have unique characteristics that grant them preference in energy and environmental policies. However, considering that the renewable resources are barely controllable and sometimes unpredictable, some challenges are faced when integrating high shares of renewable sources in power systems. In order to mitigate this problem, this paper presents a decision-making methodology regarding renewable investments. The model computes the optimal renewable generation mix from different available technologies (hydro, wind and photovoltaic) that integrates a given share of renewable sources, minimizing residual demand variability, therefore stabilizing the thermal power generation. The model also includes a spatial optimization of wind farms in order to identify the best distribution of wind capacity. This methodology is applied to the Portuguese power system.

Moisture recycling in the Iberian Peninsula from a regional climate simulation: spatiotemporal analysis and impact on the precipitation regime

The contribution of the evapotranspiration from a certain region to the precipitation over the same area is referred to as water recycling. In this paper, we explore the spatiotemporal links between the recycling mechanism and the Iberian rainfall regime. We use a 9 km resolution Weather Research and Forecasting simulation of 18 years (1990-2007) to compute local and regional recycling ratios over Iberia, at the monthly scale, through both an analytical and a numerical recycling model. In contrast to coastal areas, the interior of Iberia experiences a relative maximum of precipitation in spring, suggesting a prominent role of land-atmosphere interactions on the inland precipitation regime during this period of the year. Local recycling ratios are the highest in spring and early summer, coinciding with those areas where this spring peak of rainfall represents the absolute maximum in the annual cycle. This confirms that recycling processes are crucial to explain the Iberian spring precipitation, particularly over the eastern and northeastern sectors. Average monthly recycling values range from 0.04 in December to 0.14 in June according to the numerical model and from 0.03 in December to 0.07 in May according to the analytical procedure. Our analysis shows that the highest values of recycling are limited by the coexistence of two necessary mechanisms: (1) the availability of sufficient soil moisture and (2) the occurrence of appropriate synoptic configurations favoring the development of convective regimes. The analyzed surplus of rainfall in spring has a critical impact on agriculture over large semiarid regions of the interior of Iberia.

Optimizing the renewable generation mix in the portuguese power system based on temporal and spatial diversity

Renewable energy sources (RES) have unique characteristics that grant them preference in energy and environmental policies. However, considering that the renewable resources are barely controllable and sometimes unpredictable, some challenges are faced when integrating high shares of renewable sources in power systems. In order to mitigate this problem, this paper presents a decision-making methodology regarding renewable investments. The model computes the optimal renewable generation mix from different available technologies (hydro, wind and photovoltaic) that integrates a given share of renewable sources, minimizing residual demand variability, therefore stabilizing the thermal power generation. The model also includes a spatial optimization of wind farms in order to identify the best distribution of wind capacity. This methodology is applied to the Portuguese power system.

On the requirements of interpolating polynomials for path motion constraints

In the framework of multibody dynamics, the path motion constraint enforces that a body follows a predefined curve being its rotations with respect to the curve moving frame also prescribed. The kinematic constraint formulation requires the evaluation of the fourth derivative of the curve with respect to its arc length. Regardless of the fact that higher order polynomials lead to unwanted curve oscillations, at least a fifth order polynomials is required to formulate this constraint. From the point of view of geometric control lower order polynomials are preferred. This work shows that for multibody dynamic formulations with dependent coordinates the use of cubic polynomials is possible, being the dynamic response similar to that obtained with higher order polynomials. The stabilization of the equations of motion, always required to control the constraint violations during long analysis periods due to the inherent numerical errors of the integration process, is enough to correct the error introduced by using a lower order polynomial interpolation and thus forfeiting the analytical requirement for higher order polynomials.

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.

Hyperspectral unmixing algorithm via dependent component analysis

This paper introduces a new method to blindly unmix hyperspectral data, termed dependent component analysis (DECA). This method decomposes a hyperspectral images into a collection of reflectance (or radiance) spectra of the materials present in the scene (endmember signatures) and the corresponding abundance fractions at each pixel. DECA assumes that each pixel is a linear mixture of the endmembers signatures weighted by the correspondent abundance fractions. These abudances are modeled as mixtures of Dirichlet densities, thus enforcing the constraints on abundance fractions imposed by the acquisition process, namely non-negativity and constant sum. The mixing matrix is inferred by a generalized expectation-maximization (GEM) type algorithm. This method overcomes the limitations of unmixing methods based on Independent Component Analysis (ICA) and on geometrical based approaches. The effectiveness of the proposed method is illustrated using simulated data based on U.S.G.S. laboratory spectra and real hyperspectral data collected by the AVIRIS sensor over Cuprite, Nevada.