Analysis of Stochastic Volatility Sequences Generated by Product Autoregressive Models

The classical methods of analysing time series by Box-Jenkins approach assume that the observed series uctuates around changing levels with constant variance. That is, the time series is assumed to be of homoscedastic nature. However, the nancial time series exhibits the presence of heteroscedasticity in the sense that, it possesses non-constant conditional variance given the past observations. So, the analysis of nancial time series, requires the modelling of such variances, which may depend on some time dependent factors or its own past values. This lead to introduction of several classes of models to study the behaviour of nancial time series. See Taylor (1986), Tsay (2005), Rachev et al. (2007). The class of models, used to describe the evolution of conditional variances is referred to as stochastic volatility modelsThe stochastic models available to analyse the conditional variances, are based on either normal or log-normal distributions. One of the objectives of the present study is to explore the possibility of employing some non-Gaussian distributions to model the volatility sequences and then study the behaviour of the resulting return series. This lead us to work on the related problem of statistical inference, which is the main contribution of the thesis

Approximate approximations for the Poisson and the Stokes equations

The method of approximate approximations is based on generating functions representing an approximate partition of the unity, only. In the present paper this method is used for the numerical solution of the Poisson equation and the Stokes system in R^n (n = 2, 3). The corresponding approximate volume potentials will be computed explicitly in these cases, containing a one-dimensional integral, only. Numerical simulations show the efficiency of the method and confirm the expected convergence of essentially second order, depending on the smoothness of the data.

Surface Reflectance Recognition and Real-World Illumination Statistics

Humans distinguish materials such as metal, plastic, and paper effortlessly at a glance. Traditional computer vision systems cannot solve this problem at all. Recognizing surface reflectance properties from a single photograph is difficult because the observed image depends heavily on the amount of light incident from every direction. A mirrored sphere, for example, produces a different image in every environment. To make matters worse, two surfaces with different reflectance properties could produce identical images. The mirrored sphere simply reflects its surroundings, so in the right artificial setting, it could mimic the appearance of a matte ping-pong ball. Yet, humans possess an intuitive sense of what materials typically "look like" in the real world. This thesis develops computational algorithms with a similar ability to recognize reflectance properties from photographs under unknown, real-world illumination conditions. Real-world illumination is complex, with light typically incident on a surface from every direction. We find, however, that real-world illumination patterns are not arbitrary. They exhibit highly predictable spatial structure, which we describe largely in the wavelet domain. Although they differ in several respects from the typical photographs, illumination patterns share much of the regularity described in the natural image statistics literature. These properties of real-world illumination lead to predictable image statistics for a surface with given reflectance properties. We construct a system that classifies a surface according to its reflectance from a single photograph under unknown illuminination. Our algorithm learns relationships between surface reflectance and certain statistics computed from the observed image. Like the human visual system, we solve the otherwise underconstrained inverse problem of reflectance estimation by taking advantage of the statistical regularity of illumination. For surfaces with homogeneous reflectance properties and known geometry, our system rivals human performance.

Comparing correspondence analysis and the log-ratio alternative for representing categorical data

We compare correspondance análisis to the logratio approach based on compositional data. We also compare correspondance análisis and an alternative approach using Hellinger distance, for representing categorical data in a contingency table. We propose a coefficient which globally measures the similarity between these approaches. This coefficient can be decomposed into several components, one component for each principal dimension, indicating the contribution of the dimensions to the difference between the two representations. These three methods of representation can produce quite similar results. One illustrative example is given

Discrete and continuous compositions

This paper examines a dataset which is modeled well by the Poisson-Log Normal process and by this process mixed with Log Normal data, which are both turned into compositions. This generates compositional data that has zeros without any need for conditional models or assuming that there is missing or censored data that needs adjustment. It also enables us to model dependence on covariates and within the composition

A Log-linear model of grain size influence on the geochemistry of sediments

Sediment composition is mainly controlled by the nature of the source rock(s), and chemical (weathering) and physical processes (mechanical crushing, abrasion, hydrodynamic sorting) during alteration and transport. Although the factors controlling these processes are conceptually well understood, detailed quantification of compositional changes induced by a single process are rare, as are examples where the effects of several processes can be distinguished. The present study was designed to characterize the role of mechanical crushing and sorting in the absence of chemical weathering. Twenty sediment samples were taken from Alpine glaciers that erode almost pure granitoid lithologies. For each sample, 11 grain-size fractions from granules to clay (ø grades <-1 to >9) were separated, and each fraction was analysed for its chemical composition. The presence of clear steps in the box-plots of all parts (in adequate ilr and clr scales) against ø is assumed to be explained by typical crystal size ranges for the relevant mineral phases. These scatter plots and the biplot suggest a splitting of the full grain size range into three groups: coarser than ø=4 (comparatively rich in SiO2, Na2O, K2O, Al2O3, and dominated by “felsic” minerals like quartz and feldspar), finer than ø=8 (comparatively rich in TiO2, MnO, MgO, Fe2O3, mostly related to “mafic” sheet silicates like biotite and chlorite), and intermediate grains sizes (4≤ø <8; comparatively rich in P2O5 and CaO, related to apatite, some feldspar). To further test the absence of chemical weathering, the observed compositions were regressed against three explanatory variables: a trend on grain size in ø scale, a step function for ø≥4, and another for ø≥8. The original hypothesis was that the trend could be identified with weathering effects, whereas each step function would highlight those minerals with biggest characteristic size at its lower end. Results suggest that this assumption is reasonable for the step function, but that besides weathering some other factors (different mechanical behavior of minerals) have also an important contribution to the trend. Key words: sediment, geochemistry, grain size, regression, step function

Coherent forecasting of multiple-decrement life tables: a test using Japanese cause of death data

Planners in public and private institutions would like coherent forecasts of the components of age-specic mortality, such as causes of death. This has been di cult to achieve because the relative values of the forecast components often fail to behave in a way that is coherent with historical experience. In addition, when the group forecasts are combined the result is often incompatible with an all-groups forecast. It has been shown that cause-specic mortality forecasts are pessimistic when compared with all-cause forecasts (Wilmoth, 1995). This paper abandons the conventional approach of using log mortality rates and forecasts the density of deaths in the life table. Since these values obey a unit sum constraint for both conventional single-decrement life tables (only one absorbing state) and multiple-decrement tables (more than one absorbing state), they are intrinsically relative rather than absolute values across decrements as well as ages. Using the methods of Compositional Data Analysis pioneered by Aitchison (1986), death densities are transformed into the real space so that the full range of multivariate statistics can be applied, then back-transformed to positive values so that the unit sum constraint is honoured. The structure of the best-known, single-decrement mortality-rate forecasting model, devised by Lee and Carter (1992), is expressed in compositional form and the results from the two models are compared. The compositional model is extended to a multiple-decrement form and used to forecast mortality by cause of death for Japan

La predicci??n del rendimiento acad??mico : regresi??n lineal versus regresi??n log??stica

Resumen de los autores. Res??menes en espa??ol e ingl??s

Visual SLAM for underwater vehicles using video velocity log and natural landmarks

A visual SLAM system has been implemented and optimised for real-time deployment on an AUV equipped with calibrated stereo cameras. The system incorporates a novel approach to landmark description in which landmarks are local sub maps that consist of a cloud of 3D points and their associated SIFT/SURF descriptors. Landmarks are also sparsely distributed which simplifies and accelerates data association and map updates. In addition to landmark-based localisation the system utilises visual odometry to estimate the pose of the vehicle in 6 degrees of freedom by identifying temporal matches between consecutive local sub maps and computing the motion. Both the extended Kalman filter and unscented Kalman filter have been considered for filtering the observations. The output of the filter is also smoothed using the Rauch-Tung-Striebel (RTS) method to obtain a better alignment of the sequence of local sub maps and to deliver a large-scale 3D acquisition of the surveyed area. Synthetic experiments have been performed using a simulation environment in which ray tracing is used to generate synthetic images for the stereo system

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