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.

Dominant partial least square factors of consumer purchase behaviour of passenger cars

Globalization and liberalization, with the entry of many prominent foreign manufacturers, changed the automobile scenario in India, since early 1990’s. World Leaders in automobile manufacturing such as Ford, General Motors, Honda, Toyota, Suzuki, Hyundai, Renault, Mitsubishi, Benz, BMW, Volkswagen and Nissan set up their manufacturing units in India in joint venture with their Indian counterpart companies, by making use of the Foreign Direct Investment policy of the Government of India, These manufacturers started capturing the hearts of Indian car customers with their choice of technological and innovative product features, with quality and reliability. With the multiplicity of choices available to the Indian passenger car buyers, it drastically changed the way the car purchase scenario in India and particularly in the State of Kerala. This transformed the automobile scene from a sellers’ market to buyers’ market. Car customers started developing their own personal preferences and purchasing patterns, which were hitherto unknown in the Indian automobile segment. The main purpose of this paper is to develop a model with major variables, which influence the consumer purchase behaviour of passenger car owners in the State of Kerala. Though there are innumerable studies conducted in other countries, there are very few thesis and research work conducted to study the consumer behaviour of the passenger car industry in India and specifically in the State of Kerala. The results of the research contribute to the practical knowledge base of the automobile industry, specifically to the passenger car segment. It has also a great contributory value addition to the manufacturers and dealers for customizing their marketing plans in the State

Approximate Gauss-Newton methods for nonlinear least squares problems

The Gauss–Newton algorithm is an iterative method regularly used for solving nonlinear least squares problems. It is particularly well suited to the treatment of very large scale variational data assimilation problems that arise in atmosphere and ocean forecasting. The procedure consists of a sequence of linear least squares approximations to the nonlinear problem, each of which is solved by an “inner” direct or iterative process. In comparison with Newton’s method and its variants, the algorithm is attractive because it does not require the evaluation of second-order derivatives in the Hessian of the objective function. In practice the exact Gauss–Newton method is too expensive to apply operationally in meteorological forecasting, and various approximations are made in order to reduce computational costs and to solve the problems in real time. Here we investigate the effects on the convergence of the Gauss–Newton method of two types of approximation used commonly in data assimilation. First, we examine “truncated” Gauss–Newton methods where the inner linear least squares problem is not solved exactly, and second, we examine “perturbed” Gauss–Newton methods where the true linearized inner problem is approximated by a simplified, or perturbed, linear least squares problem. We give conditions ensuring that the truncated and perturbed Gauss–Newton methods converge and also derive rates of convergence for the iterations. The results are illustrated by a simple numerical example. A practical application to the problem of data assimilation in a typical meteorological system is presented.

On integral equation and least squares methods for scattering by diffraction gratings

In this paper we consider the scattering of a plane acoustic or electromagnetic wave by a one-dimensional, periodic rough surface. We restrict the discussion to the case when the boundary is sound soft in the acoustic case, perfectly reflecting with TE polarization in the EM case, so that the total field vanishes on the boundary. We propose a uniquely solvable first kind integral equation formulation of the problem, which amounts to a requirement that the normal derivative of the Green's representation formula for the total field vanish on a horizontal line below the scattering surface. We then discuss the numerical solution by Galerkin's method of this (ill-posed) integral equation. We point out that, with two particular choices of the trial and test spaces, we recover the so-called SC (spectral-coordinate) and SS (spectral-spectral) numerical schemes of DeSanto et al., Waves Random Media, 8, 315-414 1998. We next propose a new Galerkin scheme, a modification of the SS method that we term the SS* method, which is an instance of the well-known dual least squares Galerkin method. We show that the SS* method is always well-defined and is optimally convergent as the size of the approximation space increases. Moreover, we make a connection with the classical least squares method, in which the coefficients in the Rayleigh expansion of the solution are determined by enforcing the boundary condition in a least squares sense, pointing out that the linear system to be solved in the SS* method is identical to that in the least squares method. Using this connection we show that (reflecting the ill-posed nature of the integral equation solved) the condition number of the linear system in the SS* and least squares methods approaches infinity as the approximation space increases in size. We also provide theoretical error bounds on the condition number and on the errors induced in the numerical solution computed as a result of ill-conditioning. Numerical results confirm the convergence of the SS* method and illustrate the ill-conditioning that arises.

A theoretical adaptive model of thermal comfort – Adaptive Predicted Mean Vote (aPMV)

This paper presents in detail a theoretical adaptive model of thermal comfort based on the “Black Box” theory, taking into account factors such as culture, climate, social, psychological and behavioural adaptations, which have an impact on the senses used to detect thermal comfort. The model is called the Adaptive Predicted Mean Vote (aPMV) model. The aPMV model explains, by applying the cybernetics concept, the phenomena that the Predicted Mean Vote (PMV) is greater than the Actual Mean Vote (AMV) in free-running buildings, which has been revealed by many researchers in field studies. An Adaptive coefficient (λ) representing the adaptive factors that affect the sense of thermal comfort has been proposed. The empirical coefficients in warm and cool conditions for the Chongqing area in China have been derived by applying the least square method to the monitored onsite environmental data and the thermal comfort survey results.

Sparse multioutput radial basis function network construction using combined locally regularised orthogonal least square and D-optimality experimental design

A construction algorithm for multioutput radial basis function (RBF) network modelling is introduced by combining a locally regularised orthogonal least squares (LROLS) model selection with a D-optimality experimental design. The proposed algorithm aims to achieve maximised model robustness and sparsity via two effective and complementary approaches. The LROLS method alone is capable of producing a very parsimonious RBF network model with excellent generalisation performance. The D-optimality design criterion enhances the model efficiency and robustness. A further advantage of the combined approach is that the user only needs to specify a weighting for the D-optimality cost in the combined RBF model selecting criterion and the entire model construction procedure becomes automatic. The value of this weighting does not influence the model selection procedure critically and it can be chosen with ease from a wide range of values.

Iterative Methods for Equality-Constrained Least Squares Problems

We consider the linear equality-constrained least squares problem (LSE) of minimizing ${\|c - Gx\|}_2 $, subject to the constraint $Ex = p$. A preconditioned conjugate gradient method is applied to the Kuhn–Tucker equations associated with the LSE problem. We show that our method is well suited for structural optimization problems in reliability analysis and optimal design. Numerical tests are performed on an Alliant FX/8 multiprocessor and a Cray-X-MP using some practical structural analysis data.

Methods of Estimation in Multiple Linear Regression: Application to Clinical Data

Nesse artigo, tem-se o interesse em avaliar diferentes estratégias de estimação de parâmetros para um modelo de regressão linear múltipla. Para a estimação dos parâmetros do modelo foram utilizados dados de um ensaio clínico em que o interesse foi verificar se o ensaio mecânico da propriedade de força máxima (EM-FM) está associada com a massa femoral, com o diâmetro femoral e com o grupo experimental de ratas ovariectomizadas da raça Rattus norvegicus albinus, variedade Wistar. Para a estimação dos parâmetros do modelo serão comparadas três metodologias: a metodologia clássica, baseada no método dos mínimos quadrados; a metodologia Bayesiana, baseada no teorema de Bayes; e o método Bootstrap, baseado em processos de reamostragem.

DETERMINATION of SILICON IN LUBRICANT OIL BY HIGH-RESOLUTION CONTINUUM SOURCE FLAME ATOMIC ABSORPTION SPECTROMETRY USING LEAST-SQUARE BACKGROUND CORRECTION and INTERNAL STANDARDIZATION

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Neuroethologic differences in sleep deprivation induced by the single- and multiple-platform methods

It has been proposed that the multiple-platform method (MP) for desynchronized sleep (DS) deprivation eliminates the stress induced by social isolation and by the restriction of locomotion in the single-platform (SP) method. MP, however, induces a higher increase in plasma corticosterone and ACTH levels than SP. Since deprivation is of heuristic value to identify the functional role of this state of sleep, the objective of the present study was to determine the behavioral differences exhibited by rats during sleep deprivation induced by these two methods. All behavioral patterns exhibited by a group of 7 albino male Wistar rats submitted to 4 days of sleep deprivation by the MP method (15 platforms, spaced 150 mm apart) and by 7 other rats submitted to sleep deprivation by the SP method were recorded in order to elaborate an ethogram. The behavioral patterns were quantitated in 10 replications by naive observers using other groups of 7 rats each submitted to the same deprivation schedule. Each quantification session lasted 35 min and the behavioral patterns presented by each rat over a period of 5 min were counted. The results obtained were: a) rats submitted to the MP method changed platforms at a mean rate of 2.62 ± 1.17 platforms h-1 animal-1; b) the number of episodes of noninteractive waking patterns for the MP animals was significantly higher than that for SP animals (1077 vs 768); c) additional episodes of waking patterns (26.9 ± 18.9 episodes/session) were promoted by social interaction in MP animals; d) the cumulative number of sleep episodes observed in the MP test (311) was significantly lower (chi-square test, 1 d.f., P<0.05) than that observed in the SP test (534); e) rats submitted to the MP test did not show the well-known increase in ambulatory activity observed after the end of the SP test; f) comparison of 6 MP and 6 SP rats showed a significantly shorter latency to the onset of DS in MP rats (7.8 ± 4.3 and 29.0 ± 25.0 min, respectively; Student t-test, P<0.05). We conclude that the social interaction occurring in the MP test generates additional stress since it increases the time of forced wakefulness and reduces the time of rest promoted by synchronized sleep.

The Brazilian Research Consortium on Obsessive-Compulsive Spectrum Disorders: recruitment, assessment instruments, methods for the development of multicenter collaborative studies and preliminary results

OBJETIVO: Descrever o recrutamento de pacientes, instrumentos de avaliação, métodos para o desenvolvimento de estudos colaborativos multicêntricos e os resultados preliminares do Consórcio Brasileiro de Pesquisa em Transtornos do Espectro Obsessivo-Compulsivo, que inclui sete centros universitários. MÉTODO: Este estudo transversal incluiu entrevistas semi-estruturadas (dados sociodemográficos, histórico médico e psiquiátrico, curso da doença e diagnósticos psiquiátricos comórbidos) e instrumentos que avaliam os sintomas do transtorno obsessivo-compulsivo (Escala para Sintomas Obsessivo-Compulsivos de Yale-Brown e Escala Dimensional para Sintomas Obsessivo-Compulsivos de Yale-Brown), sintomas depressivos (Inventário de Depressão de Beck), sintomas ansiosos (Inventário de Ansiedade de Beck), fenômenos sensoriais (Escala de Fenômenos Sensoriais da Universidade de São Paulo), juízo crítico (Escala de Avaliação de Crenças de Brown), tiques (Escala de Gravidade Global de Tiques de Yale) e qualidade de vida (questionário genérico de avaliação de qualidade de vida, Medical Outcome Quality of Life Scale Short-form-36 e Escala de Avaliação Social). O treinamento dos avaliadores consistiu em assistir cinco entrevistas filmadas e entrevistar cinco pacientes junto com um pesquisador mais experiente, antes de entrevistar pacientes sozinhos. A confiabilidade entre todos os líderes de grupo para os instrumentos mais importantes (Structured Clinical Interview for DSM-IV, Dimensional Yale-Brown Obsessive-Compulsive Scale, Universidade de São Paulo Sensory Phenomena Scale ) foi medida após seis entrevistas completas. RESULTADOS: A confiabilidade entre avaliadores foi de 96%. Até março de 2008, 630 pacientes com transtorno obsessivo-compulsivo tinham sido sistematicamente avaliados. A média de idade (±SE) foi de 34,7 (±0,51), 56,3% eram do sexo feminino e 84,6% caucasianos. Os sintomas obsessivo-compulsivos mais prevalentes foram os de simetria e os de contaminação. As comorbidades psiquiátricas mais comuns foram depressão maior, ansiedade generalizada e transtorno de ansiedade social. O transtorno de controle de impulsos mais comum foi escoriação neurótica. CONCLUSÃO: Este consórcio de pesquisa, pioneiro no Brasil, permitiu delinear o perfil sociodemográfico, clínico e terapêutico do paciente com transtorno obsessivo-compulsivo em uma grande amostra clínica de pacientes. O Consórcio Brasileiro de Pesquisa em Transtornos do Espectro Obsessivo-Compulsivo estabeleceu uma importante rede de colaboração de investigação clínica padronizada sobre o transtorno obsessivo-compulsivo e pode abrir o caminho para projetos semelhantes destinados a integrar outros grupos de pesquisa no Brasil e em todo o mundo.

Effect of surface conditioning methods on the microtensile bond strength of resin composite to composite after aging conditions

Objectives. This study evaluated the effect of two different surface conditioning methods on the repair bond strength of a bis-GMA-adduct/bis-EMA/TEGDMA based resin composite after three aging conditions.Methods. Thirty-six composite resin blocks (Esthet X, Dentsply) were prepared (5 mm x 6 mm x 6 mm) and randomly assigned into three groups for aging process: (a) immersion in citric acid (pH 3.0 at 37 degrees C, 1 week) (CA); (b) boiling in water for 8h (BW) and (c) thermocycling (x5000, 5-55 degrees C, dwell time: 30s) (TC). After aging, the blocks were assigned to one of the following surface conditioning methods: (1) silica coating (30 mu m SiOx) (CoJet, 3M ESPE) + silane (ESPE-Sil) (CJ), (2) phosphoric acid + adhesive resin (Single Bond, 3M ESPE) (PA). Resin composite (Esthet.X (R)) was bonded to the conditioned substrates incrementally and light polymerized. The experimental groups formed were as follows: Gr1:CA + PA; Gr2:CA + CJ Gr3:BW + PA; Gr4: BW + CJ; Gr5:TC + PA; Gr6: TC + CJ. The specimens were sectioned in two axes (x and y) with a diamond disc under coolant irrigation in order to obtain non-trimmed bar specimens (sticks, 10 mm x 1 mm x 1 mm) with 1 mm(2) of bonding area. The microtensile test was accomplished in a universal testing machine (crosshead speed: 0.5 mm min(-1)).Results. The means and standard deviations of bond strength (MPa +/- S.D.) per group were as follows: Gr1: 25.5 +/- 10.3; Gr2: 46.3 +/- 10.1; Gr3: 21.7 +/- 7.1; Gr4: 52.3 +/- 15.1; GrS: 16.1 +/- 5.1; Gr6, 49.6 +/- 13.5. The silica coated groups showed significantly higher mean bond values after all three aging conditions (p < 0.0001) (two-way ANOVA and Tukey tests, alpha = 0.05). The interaction effect revealed significant influence of TC aging on both silica coated and acid etched groups compared to the other aging methods (p < 0.032). Citric acid was the least aggressive aging medium.Significance. Chairside silica coating and silanization provided higher resin-resin bond strength values compared to acid etching with phosphoric acid followed by adhesive resin applications. Thermocycling the composite substrates resulted in the lowest repair bond strength compared to citric acid challenge or boiling in water. (C) 2006 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.

Monitoring process mean and variability with one non-central chi-square chart

Traditionally, an (X) over bar -chart is used to control the process mean and an R-chart to control the process variance. However, these charts are not sensitive to small changes in process parameters. A good alternative to these charts is the exponentially weighted moving average (EWMA) control chart for controlling the process mean and variability, which is very effective in detecting small process disturbances. In this paper, we propose a single chart that is based on the non-central chi-square statistic, which is more effective than the joint (X) over bar and R charts in detecting assignable cause(s) that change the process mean and/or increase variability. It is also shown that the EWMA control chart based on a non-central chi-square statistic is more effective in detecting both increases and decreases in mean and/or variability.