Modeling and Analysis of Some Heavy Tailed Time Series

The thesis has covered various aspects of modeling and analysis of finite mean time series with symmetric stable distributed innovations. Time series analysis based on Box and Jenkins methods are the most popular approaches where the models are linear and errors are Gaussian. We highlighted the limitations of classical time series analysis tools and explored some generalized tools and organized the approach parallel to the classical set up. In the present thesis we mainly studied the estimation and prediction of signal plus noise model. Here we assumed the signal and noise follow some models with symmetric stable innovations.We start the thesis with some motivating examples and application areas of alpha stable time series models. Classical time series analysis and corresponding theories based on finite variance models are extensively discussed in second chapter. We also surveyed the existing theories and methods correspond to infinite variance models in the same chapter. We present a linear filtering method for computing the filter weights assigned to the observation for estimating unobserved signal under general noisy environment in third chapter. Here we consider both the signal and the noise as stationary processes with infinite variance innovations. We derived semi infinite, double infinite and asymmetric signal extraction filters based on minimum dispersion criteria. Finite length filters based on Kalman-Levy filters are developed and identified the pattern of the filter weights. Simulation studies show that the proposed methods are competent enough in signal extraction for processes with infinite variance.Parameter estimation of autoregressive signals observed in a symmetric stable noise environment is discussed in fourth chapter. Here we used higher order Yule-Walker type estimation using auto-covariation function and exemplify the methods by simulation and application to Sea surface temperature data. We increased the number of Yule-Walker equations and proposed a ordinary least square estimate to the autoregressive parameters. Singularity problem of the auto-covariation matrix is addressed and derived a modified version of the Generalized Yule-Walker method using singular value decomposition.In fifth chapter of the thesis we introduced partial covariation function as a tool for stable time series analysis where covariance or partial covariance is ill defined. Asymptotic results of the partial auto-covariation is studied and its application in model identification of stable auto-regressive models are discussed. We generalize the Durbin-Levinson algorithm to include infinite variance models in terms of partial auto-covariation function and introduce a new information criteria for consistent order estimation of stable autoregressive model.In chapter six we explore the application of the techniques discussed in the previous chapter in signal processing. Frequency estimation of sinusoidal signal observed in symmetric stable noisy environment is discussed in this context. Here we introduced a parametric spectrum analysis and frequency estimate using power transfer function. Estimate of the power transfer function is obtained using the modified generalized Yule-Walker approach. Another important problem in statistical signal processing is to identify the number of sinusoidal components in an observed signal. We used a modified version of the proposed information criteria for this purpose.

Geodynamics of the Andaman - Sumatra - Java Trench - Arc System Based on Gravity and Seismotectonic Study

This work aims to study the variation in subduction zone geometry along and across the arc and the fault pattern within the subducting plate. Depth of penetration as well as the dip of the Benioff zone varies considerably along the arc which corresponds to the curvature of the fold- thrust belt which varies from concave to convex in different sectors of the arc. The entire arc is divided into 27 segments and depth sections thus prepared are utilized to investigate the average dip of the Benioff zone in the different parts of the entire arc, penetration depth of the subducting lithosphere, the subduction zone geometry underlying the trench, the arctrench gap, etc.The study also describes how different seismogenic sources are identified in the region, estimation of moment release rate and deformation pattern. The region is divided into broad seismogenic belts. Based on these previous studies and seismicity Pattern, we identified several broad distinct seismogenic belts/sources. These are l) the Outer arc region consisting of Andaman-Nicobar islands 2) the back-arc Andaman Sea 3)The Sumatran fault zone(SFZ)4)Java onshore region termed as Jave Fault Zone(JFZ)5)Sumatran fore arc silver plate consisting of Mentawai fault(MFZ)6) The offshore java fore arc region 7)The Sunda Strait region.As the Seismicity is variable,it is difficult to demarcate individual seismogenic sources.Hence, we employed a moving window method having a window length of 3—4° and with 50% overlapping starting from one end to the other. We succeeded in defining 4 sources each in the Andaman fore arc and Back arc region, 9 such sources (moving windows) in the Sumatran Fault zone (SFZ), 9 sources in the offshore SFZ region and 7 sources in the offshore Java region. Because of the low seismicity along JFZ, it is separated into three seismogenic sources namely West Java, Central Java and East Java. The Sunda strait is considered as a single seismogenic source.The deformation rates for each of the seismogenic zones have been computed. A detailed error analysis of velocity tensors using Monte—Carlo simulation method has been carried out in order to obtain uncertainties. The eigen values and the respective eigen vectors of the velocity tensor are computed to analyze the actual deformation pattem for different zones. The results obtained have been discussed in the light of regional tectonics, and their implications in terms of geodynamics have been enumerated.ln the light of recent major earthquakes (26th December 2004 and 28th March 2005 events) and the ongoing seismic activity, we have recalculated the variation in the crustal deformation rates prior and after these earthquakes in Andaman—Sumatra region including the data up to 2005 and the significant results has been presented.ln this chapter, the down going lithosphere along the subduction zone is modeled using the free air gravity data by taking into consideration the thickness of the crustal layer, the thickness of the subducting slab, sediment thickness, presence of volcanism, the proximity of the continental crust etc. Here a systematic and detailed gravity interpretation constrained by seismicity and seismic data in the Andaman arc and the Andaman Sea region in order to delineate the crustal structure and density heterogeneities a Io nagnd across the arc and its correlation with the seismogenic behaviour is presented.

Transition metal complexes derived from ketone based N(4)-substituted thiosemicarbazones: Crystal structures and spectral studies

Thiosemicarbazones have recently attracted considerable attention due to their ability to form tridentate chelates with transition metal ions through either two nitrogen and sulfur atoms, N–N–S or oxygen, nitrogen and sulfur atoms, O–N–S. Considerable interest in thiosemicarbazones and their transition metal complexes has also grown in the areas of biology and chemistry due to biological activities such as antitumoral, fungicidal, bactericidal, antiviral and nonlinear optical properties. They have been used for metal analyses, for device applications related to telecommunications, optical computing, storage and information processing.The versatile applications of metal complexes of thiosemicarbazones in various fields prompted us to synthesize the tridentate NNS-donor thiosemicarbazones and their metal complexes. As a part of our studies on transition metal complexes with these ligands, the researcher undertook the current work with the following objectives. 1. To synthesize and physico-chemically characterize the following thiosemicarbazone ligands: a. Di-2-pyridyl ketone-N(4)-methyl thiosemicarbazone (HDpyMeTsc) b. Di-2-pyridyl ketone-N(4)-ethyl thiosemicarbazone (HDpyETsc) 2. To synthesize oxovanadium(IV), manganese(II), nickel(II), copper(II), zinc(II) and cadmium(II) complexes using the synthesized thiosemicarbazones as principal ligands and some anionic coligands. 3. To study the coordination modes of the ligands in metal complexes by using different physicochemical methods like partial elemental analysis, thermogravimetry and by different spectroscopic techniques. 4. To establish the structure of compounds by single crystal XRD studies

Studies on some aspects of wave propagation through nonlinear media

Nonlinearity is a charming element of nature and Nonlinear Science has now become one of the most important tools for the fundamental understanding of the nature. Solitons— solutions of a class of nonlinear partial differential equations — which propagate without spreading and having particle— like properties represent one of the most striking aspects of nonlinear phenomena. The study of wave propagation through nonlinear media has wide applications in different branches of physics.Different mathematical techniques have been introduced to study nonlinear systems. The thesis deals with the study of some of the aspects of electromagnetic wave propagation through nonlinear media, viz, plasma and ferromagnets, using reductive perturbation method. The thesis contains 6 chapters

Studies On The Synthesis Of Vitamin A And Related Compounds

In the present work different new approaches for the synthesis of Vitamin A are investigated. In these synthetic schemes, all the twenty carbon atoms of the target molecule are derived either fully from components isolated from common essential oils or partially from commercially available materials. By retrosynthetic analysis, Vitamin A molecule can be disconnected into a cyclic and a linear unit. Different methods for the synthesis of the linear and the cyclic components are described. The monoterpenes, geraniol and citral, major constituents of palmarosa and lemongrass oils, have the required basic carbon framework for consideration as starting materials for the synthesis of Vitamin A. The potential of these easily available naturally occurring compounds as promising starting materials for Vitamin A synthesis is demonstrated. Organoselenium and organosulfur mediated functional group transformations for the synthesis of the functionalised conjugated C10 linear components (ie., the dimethyloctatriene derivatives) are reported. The classical approaches as well as the attempted preparation of cyclic C10 and C13 units employed in the present study as intermediates for Vitamin A synthesis are described. The utility of commercially available materials namely 2-acetylbutyrolactone and levulinic acid in -the preparation of C5 intermediates for Vitamin A synthesis is demonstrated.

Spatial and Temporal Variation of Microbial Population in the Grassland Soils of Tropical Montane Forest: Influence of Soil Physico-Chemical Characteristics and Nutrients

Present study is focused on the spatiotemporal variation of the microbial population (bacteria, fungus and actinomycetes) in the grassland soils of tropical montane forest and its relation with important soil physico-chemical characteristics and nutrients. Different physico-chemical properties of the soil such as temperature, moisture content, organic carbon, available nitrogen, available phosphorous and available potassium have been studied. Results of the present study revealed that both microbial load and soil characteristics showed spatiotemporal variation. Microbial population of the grassland soils were characterized by high load of bacteria followed by fungus and actinomycetes. Microbial load was high during pre monsoon season, followed by post monsoon and monsoon. The microbial load varied with important soil physico-chemical properties and nutrients. Organic carbon content, available nitrogen and available phosphorous were positively correlated with bacterial load and the correlation is significant at 0.05 and 0.01 levels respectively. Available nitrogen and available phosphorous were positively correlated with fungus at 0.05 level significance. Moisture content was negatively correlated with actinomycetes at 0.01 level of significance. Organic carbon negatively correlated with actinomycetes load at 0.05 level of significance

Length-weight relationship, relative condition factor (Kn) and morphometry of Arius subrostratus (Valenciennes, 1840) from a coastal wetland in Kerala

The length – weight relationship and relative condition factor of the shovel nose catfish, Arius subrostratus (Valenciennes, 1840) from Champakkara backwater were studied by examination of 392 specimens collected during June to September 2008. These fishes ranged from 6 to 29 cm in total length and 5.6 to 218 g in weight. The relation between the total length and weight of Arius subrostratus is described as Log W = -1.530+2.6224 log L for males, Log W = - 2.131 + 3.0914 log L for females and Log W = - 1.742 + 2.8067 log L for sexes combined. The mean relative condition factor (Kn) values ranged from 0.75 to 1.07 for males, 0.944 to 1.407 for females and 0.96 to 1.196 for combined sexes. The length-weight relationship and relative condition factor showed that the well-being of A. subrostratus is good. The morphometric measurements of various body parts and meristic counts were recorded. The morphometric measurements were found to be non-linear and there is no significant difference observed between the two sexes. From the present investigation, the fin formula can be written as D: I, 7; P: I, 12; A: 17 – 20; C: 26 – 32. There is no change in meristic counts with the increase in body length.

Experimentelle und numerische Untersuchungen zur Dispersion von Dichteströmungen in einem stochastischen Modellaquifer

Es ist bekannt, dass die Dichte eines gelösten Stoffes die Richtung und die Stärke seiner Bewegung im Untergrund entscheidend bestimmen kann. Eine Vielzahl von Untersuchungen hat gezeigt, dass die Verteilung der Durchlässigkeiten eines porösen Mediums diese Dichteffekte verstärken oder abmindern kann. Wie sich dieser gekoppelte Effekt auf die Vermischung zweier Fluide auswirkt, wurde in dieser Arbeit untersucht und dabei das experimentelle sowohl mit dem numerischen als auch mit dem analytischen Modell gekoppelt. Die auf der Störungstheorie basierende stochastische Theorie der macrodispersion wurde in dieser Arbeit für den Fall der transversalen Makodispersion. Für den Fall einer stabilen Schichtung wurde in einem Modelltank (10m x 1.2m x 0.1m) der Universität Kassel eine Serie sorgfältig kontrollierter zweidimensionaler Experimente an einem stochastisch heterogenen Modellaquifer durchgeführt. Es wurden Versuchsreihen mit variierenden Konzentrationsdifferenzen (250 ppm bis 100 000 ppm) und Strömungsgeschwindigkeiten (u = 1 m/ d bis 8 m/d) an drei verschieden anisotrop gepackten porösen Medien mit variierender Varianzen und Korrelationen der lognormal verteilten Permeabilitäten durchgeführt. Die stationäre räumliche Konzentrationsausbreitung der sich ausbreitenden Salzwasserfahne wurde anhand der Leitfähigkeit gemessen und aus der Höhendifferenz des 84- und 16-prozentigen relativen Konzentrationsdurchgang die Dispersion berechnet. Parallel dazu wurde ein numerisches Modell mit dem dichteabhängigen Finite-Elemente-Strömungs- und Transport-Programm SUTRA aufgestellt. Mit dem kalibrierten numerischen Modell wurden Prognosen für mögliche Transportszenarien, Sensitivitätsanalysen und stochastische Simulationen nach der Monte-Carlo-Methode durchgeführt. Die Einstellung der Strömungsgeschwindigkeit erfolgte - sowohl im experimentellen als auch im numerischen Modell - über konstante Druckränder an den Ein- und Auslauftanks. Dabei zeigte sich eine starke Sensitivität der räumlichen Konzentrationsausbreitung hinsichtlich lokaler Druckvariationen. Die Untersuchungen ergaben, dass sich die Konzentrationsfahne mit steigendem Abstand von der Einströmkante wellenförmig einem effektiven Wert annähert, aus dem die Makrodispersivität ermittelt werden kann. Dabei zeigten sich sichtbare nichtergodische Effekte, d.h. starke Abweichungen in den zweiten räumlichen Momenten der Konzentrationsverteilung der deterministischen Experimente von den Erwartungswerten aus der stochastischen Theorie. Die transversale Makrodispersivität stieg proportional zur Varianz und Korrelation der lognormalen Permeabilitätsverteilung und umgekehrt proportional zur Strömungsgeschwindigkeit und Dichtedifferenz zweier Fluide. Aus dem von Welty et al. [2003] mittels Störungstheorie entwickelten dichteabhängigen Makrodispersionstensor konnte in dieser Arbeit die stochastische Formel für die transversale Makrodispersion weiter entwickelt und - sowohl experimentell als auch numerisch - verifiziert werden.

Managing Quality Properties of Web Service Compositions

Web services from different partners can be combined to applications that realize a more complex business goal. Such applications built as Web service compositions define how interactions between Web services take place in order to implement the business logic. Web service compositions not only have to provide the desired functionality but also have to comply with certain Quality of Service (QoS) levels. Maximizing the users' satisfaction, also reflected as Quality of Experience (QoE), is a primary goal to be achieved in a Service-Oriented Architecture (SOA). Unfortunately, in a dynamic environment like SOA unforeseen situations might appear like services not being available or not responding in the desired time frame. In such situations, appropriate actions need to be triggered in order to avoid the violation of QoS and QoE constraints. In this thesis, proper solutions are developed to manage Web services and Web service compositions with regard to QoS and QoE requirements. The Business Process Rules Language (BPRules) was developed to manage Web service compositions when undesired QoS or QoE values are detected. BPRules provides a rich set of management actions that may be triggered for controlling the service composition and for improving its quality behavior. Regarding the quality properties, BPRules allows to distinguish between the QoS values as they are promised by the service providers, QoE values that were assigned by end-users, the monitored QoS as measured by our BPR framework, and the predicted QoS and QoE values. BPRules facilitates the specification of certain user groups characterized by different context properties and allows triggering a personalized, context-aware service selection tailored for the specified user groups. In a service market where a multitude of services with the same functionality and different quality values are available, the right services need to be selected for realizing the service composition. We developed new and efficient heuristic algorithms that are applied to choose high quality services for the composition. BPRules offers the possibility to integrate multiple service selection algorithms. The selection algorithms are applicable also for non-linear objective functions and constraints. The BPR framework includes new approaches for context-aware service selection and quality property predictions. We consider the location information of users and services as context dimension for the prediction of response time and throughput. The BPR framework combines all new features and contributions to a comprehensive management solution. Furthermore, it facilitates flexible monitoring of QoS properties without having to modify the description of the service composition. We show how the different modules of the BPR framework work together in order to execute the management rules. We evaluate how our selection algorithms outperform a genetic algorithm from related research. The evaluation reveals how context data can be used for a personalized prediction of response time and throughput.

Modeling Stock Order Flows and Learning Market-Making from Data

Stock markets employ specialized traders, market-makers, designed to provide liquidity and volume to the market by constantly supplying both supply and demand. In this paper, we demonstrate a novel method for modeling the market as a dynamic system and a reinforcement learning algorithm that learns profitable market-making strategies when run on this model. The sequence of buys and sells for a particular stock, the order flow, we model as an Input-Output Hidden Markov Model fit to historical data. When combined with the dynamics of the order book, this creates a highly non-linear and difficult dynamic system. Our reinforcement learning algorithm, based on likelihood ratios, is run on this partially-observable environment. We demonstrate learning results for two separate real stocks.

Support Vector Machines: Training and Applications

The Support Vector Machine (SVM) is a new and very promising classification technique developed by Vapnik and his group at AT&T Bell Labs. This new learning algorithm can be seen as an alternative training technique for Polynomial, Radial Basis Function and Multi-Layer Perceptron classifiers. An interesting property of this approach is that it is an approximate implementation of the Structural Risk Minimization (SRM) induction principle. The derivation of Support Vector Machines, its relationship with SRM, and its geometrical insight, are discussed in this paper. Training a SVM is equivalent to solve a quadratic programming problem with linear and box constraints in a number of variables equal to the number of data points. When the number of data points exceeds few thousands the problem is very challenging, because the quadratic form is completely dense, so the memory needed to store the problem grows with the square of the number of data points. Therefore, training problems arising in some real applications with large data sets are impossible to load into memory, and cannot be solved using standard non-linear constrained optimization algorithms. We present a decomposition algorithm that can be used to train SVM's over large data sets. The main idea behind the decomposition is the iterative solution of sub-problems and the evaluation of, and also establish the stopping criteria for the algorithm. We present previous approaches, as well as results and important details of our implementation of the algorithm using a second-order variant of the Reduced Gradient Method as the solver of the sub-problems. As an application of SVM's, we present preliminary results we obtained applying SVM to the problem of detecting frontal human faces in real images.

Causes and Effects of Chaos

Most of the recent literature on chaos and nonlinear dynamics is written either for popular science magazine readers or for advanced mathematicians. This paper gives a broad introduction to this interesting and rapidly growing field at a level that is between the two. The graphical and analytical tools used in the literature are explained and demonstrated, the rudiments of the current theory are outlined and that theory is discussed in the context of several examples: an electronic circuit, a chemical reaction and a system of satellites in the solar system.

Correlación SO2/FiO2 con PaO2/FiO2 en niños en ventilación mecánica a grandes alturas : estudio multicéntrico

Cambios en la PaO2 se correlacionan de manera positiva con cambios en la SO2 permitiendo determinar la severidad de la hipoxemia. La búsqueda de un predictor que de forma no invasiva detecte pacientes con mayor compromiso pulmonar ha ganando auge; estableciendo los grados de hipoxemia moderada o severa como criterios para LPA y SDRA, a partir de los valores de PaO2/FiO2 y su correlación con la SO2/FiO2. No se conocen los valores de SO2/FiO2 que a más de 2500msnm permitan identificar la severidad de la hipoxemia en pediatría. Metodología: estudio de correlación y predicción en pacientes de un mes a 18 años de edad admitidos a UCIP, con soporte ventilatorio mecánico y análisis de gases arteriales seriados en dos Hospitales de referencia. Análisis de relación lineal y determinación de la correlación SOFiO2 y PaFiO2 a partir de 430 mediciones. Resultados: el estudio mostro una media para PaO2/FiO2 de 192,12 (DS+75,62) y para SO2/FiO2 de 208,61 (DS+62,79). La correlación SO2/FiO2 y Pa/FiO2 fue positiva y moderada-alta (r= 0,702;p<0.01). A partir de la regresión lineal entre las variables se obtuvo la ecuación de determinación PaO2/FiO2 = (0.92xSO2/FIO2) - 12, con sensibilidad y especificidad de 76% para detectar hipoxemia severa (SO2/FiO2<231), y sensibilidad de 74% y especificidad de 71% para hipoxemia moderada (SO2/FiO2<340). Discusión: los hallazgos obtenidos son muy útiles desde el punto de vista clínico para detectar rápidamente pacientes con hipoxemia moderada y severa, con riesgo potencial de deterioro, cuando no se dispone de línea arterial ó gases arteriales.

Los conceptos de salud financiera, riesgo y epidemiología en los estados financieros de las compañías del sector de extracción de petróleo crudo y gas natural en Colombia

El presente proyecto tiene como objeto identificar cuáles son los conceptos de salud, enfermedad, epidemiología y riesgo aplicables a las empresas del sector de extracción de petróleo y gas natural en Colombia. Dado, el bajo nivel de predicción de los análisis financieros tradicionales y su insuficiencia, en términos de inversión y toma de decisiones a largo plazo, además de no considerar variables como el riesgo y las expectativas de futuro, surge la necesidad de abordar diferentes perspectivas y modelos integradores. Esta apreciación es pertinente dentro del sector de extracción de petróleo y gas natural, debido a la creciente inversión extranjera que ha reportado, US$2.862 millones en el 2010, cifra mayor a diez veces su valor en el año 2003. Así pues, se podrían desarrollar modelos multi-dimensional, con base en los conceptos de salud financiera, epidemiológicos y estadísticos. El termino de salud y su adopción en el sector empresarial, resulta útil y mantiene una coherencia conceptual, evidenciando una presencia de diferentes subsistemas o factores interactuantes e interconectados. Es necesario mencionar también, que un modelo multidimensional (multi-stage) debe tener en cuenta el riesgo y el análisis epidemiológico ha demostrado ser útil al momento de determinarlo e integrarlo en el sistema junto a otros conceptos, como la razón de riesgo y riesgo relativo. Esto se analizará mediante un estudio teórico-conceptual, que complementa un estudio previo, para contribuir al proyecto de finanzas corporativas de la línea de investigación en Gerencia.

Análisis del impacto del tamaño de los activos en la cuenta de resultados mediante la utilización de espacios de fase y análisis de recurrencia

Los resultados financieros de las organizaciones son objeto de estudio y análisis permanente, predecir sus comportamientos es una tarea permanente de empresarios, inversionistas, analistas y académicos. En el presente trabajo se explora el impacto del tamaño de los activos (valor total de los activos) en la cuenta de resultados operativos y netos, analizando inicialmente la relación entre dichas variables con indicadores tradicionales del análisis financiero como es el caso de la rentabilidad operativa y neta y con elementos de estadística descriptiva que permiten calificar los datos utilizados como lineales o no lineales. Descubriendo posteriormente que los resultados financieros de las empresas vigiladas por la Superintendencia de Sociedades para el año 2012, tienen un comportamiento no lineal, de esta manera se procede a analizar la relación de los activos y los resultados con la utilización de espacios de fase y análisis de recurrencia, herramientas útiles para sistemas caóticos y complejos. Para el desarrollo de la investigación y la revisión de la relación entre las variables de activos y resultados financieros se tomó como fuente de información los reportes financieros del cierre del año 2012 de la Superintendencia de Sociedades (Superintendencia de Sociedades, 2012).