Inference for nonparametric high-frequency estimators with an application to time variation in betas

We consider the problem of conducting inference on nonparametric high-frequency estimators without knowing their asymptotic variances. We prove that a multivariate subsampling method achieves this goal under general conditions that were not previously available in the literature. We suggest a procedure for a data-driven choice of the bandwidth parameters. Our simulation study indicates that the subsampling method is much more robust than the plug-in method based on the asymptotic expression for the variance. Importantly, the subsampling method reliably estimates the variability of the Two Scale estimator even when its parameters are chosen to minimize the finite sample Mean Squared Error; in contrast, the plugin estimator substantially underestimates the sampling uncertainty. By construction, the subsampling method delivers estimates of the variance-covariance matrices that are always positive semi-definite. We use the subsampling method to study the dynamics of financial betas of six stocks on the NYSE. We document significant variation in betas within year 2006, and find that tick data captures more variation in betas than the data sampled at moderate frequencies such as every five or twenty minutes. To capture this variation we estimate a simple dynamic model for betas. The variance estimation is also important for the correction of the errors-in-variables bias in such models. We find that the bias corrections are substantial, and that betas are more persistent than the naive estimators would lead one to believe.

Significance of Time Scales in Nonlinear Dynamical Analysis of Electroencephalogram Signals

We propose to show in this paper, that the time series obtained from biological systems such as human brain are invariably nonstationary because of different time scales involved in the dynamical process. This makes the invariant parameters time dependent. We made a global analysis of the EEG data obtained from the eight locations on the skull space and studied simultaneously the dynamical characteristics from various parts of the brain. We have proved that the dynamical parameters are sensitive to the time scales and hence in the study of brain one must identify all relevant time scales involved in the process to get an insight in the working of brain.

Studies on Chaos and Synchronization in ac-driven Josephson junctions

The main goal of this thesis is to study the dynamics of Josephson junction system in the presence of an external rf-biasing.A system of two chaotically synchronized Josephson junction is studied.The change in the dynamics of the system in the presence of at phase difference between the applied fields is considered. Control of chaos is very important from an application point of view. The role Of phase difference in controlling chaos is discussed.An array of three Josephson junctions iS studied for the effect of phase difference on chaos and synchronization and the argument is extended for a system of N Josephson junctions. In the presence of a phase difference between the external fields, the system exhibits periodic behavior with a definite phase relationship between all the three junctions.Itdeals with an array of three Josephson junctions with a time delay in the coupling term. It is observed that only the outer systems synchronize while the middle system remain uncorrelated with t-he other two. The effect of phase difference between the applied fields and time-delay on system dynamics and synchronization is also studied. We study the influence of an applied ac biasing on a serniannular Josephson junction. It is found the magnetic field along with the biasing induces creation and annihilation of fluxons in the junction. The I-V characteristics of the junction is studied by considering the surface loss term also in the model equation. The system is found to exhibit chaotic behavior in the presence of ac biasing.

Studies on Quasinormal Modes and Late-time Tails in Black Hole Spacetimes

This thesis Entitled Studies on Quasinormal modes and Late-time tails black hole spacetimes. In this thesis, the signature of these new theories are probed on the evolution of field perturbations on the black hole spacetimes in the theory. Chapter 1 gives a general introduction to black holes and its perturbation formalism. Various concepts in the area covered by the thesis are also elucidated in this chapter. Chapter 2 describes the evolution of massive, charged scalar field perturbations around a Reissner-Nordstrom black hole surrounded by a static and spherically symmetric quintessence. Chapter 3 comprises the evolution of massless scalar, electromagnetic and gravitational fields around spherically symmetric black hole whose asymptotes are defined by the quintessence, with special interest on the late-time behavior. Chapter 4 examines the evolution of Dirac field around a Schwarzschild black hole surrounded by quintessence. Detailed numerical simulations are done to analyze the nature of field on different surfaces of constant radius . Chapter 5is dedicated to the study of the evolution of massless fields around the black hole geometry in the HL gravity.

Some bivariate life time models in discrete time"

The term reliability of an equipment or device is often meant to indicate the probability that it carries out the functions expected of it adequately or without failure and within specified performance limits at a given age for a desired mission time when put to use under the designated application and operating environmental stress. A broad classification of the approaches employed in relation to reliability studies can be made as probabilistic and deterministic, where the main interest in the former is to device tools and methods to identify the random mechanism governing the failure process through a proper statistical frame work, while the latter addresses the question of finding the causes of failure and steps to reduce individual failures thereby enhancing reliability. In the probabilistic attitude to which the present study subscribes to, the concept of life distribution, a mathematical idealisation that describes the failure times, is fundamental and a basic question a reliability analyst has to settle is the form of the life distribution. It is for no other reason that a major share of the literature on the mathematical theory of reliability is focussed on methods of arriving at reasonable models of failure times and in showing the failure patterns that induce such models. The application of the methodology of life time distributions is not confined to the assesment of endurance of equipments and systems only, but ranges over a wide variety of scientific investigations where the word life time may not refer to the length of life in the literal sense, but can be concieved in its most general form as a non-negative random variable. Thus the tools developed in connection with modelling life time data have found applications in other areas of research such as actuarial science, engineering, biomedical sciences, economics, extreme value theory etc.

Time misalignments in fault detection and diagnosis

El desalineamiento temporal es la incorrespondencia de dos señales debido a una distorsión en el eje temporal. La Detección y Diagnóstico de Fallas (Fault Detection and Diagnosis-FDD) permite la detección, el diagnóstico y la corrección de fallos en un proceso. La metodología usada en FDD está dividida en dos categorías: técnicas basadas en modelos y no basadas en modelos. Esta tesis doctoral trata sobre el estudio del efecto del desalineamiento temporal en FDD. Nuestra atención se enfoca en el análisis y el diseño de sistemas FDD en caso de problemas de comunicación de datos, como retardos y pérdidas. Se proponen dos técnicas para reducir estos problemas: una basada en programación dinámica y la otra en optimización. Los métodos propuestos han sido validados sobre diferentes sistemas dinámicos: control de posición de un motor de corriente continua, una planta de laboratorio y un problema de sistemas eléctricos conocido como hueco de tensión.

An evaluation of different growth functions for describing the profile of live weight with time (age) in meat and egg strains of chicken

A total of 86 profiles from meat and egg strains of chickens (male and female) were used in this study. Different flexible growth functions were evaluated with regard to their ability to describe the relationship between live weight and age and were compared with the Gompertz and logistic equations, which have a fixed point of inflection. Six growth functions were used: Gompertz, logistic, Lopez, Richards, France, and von Bertalanffy. A comparative analysis was carried out based on model behavior and statistical performance. The results of this study confirmed the initial concern about the limitation of a fixed point of inflection, such as in the Gompertz equation. Therefore, consideration of flexible growth functions as an alternatives to the simpler equations (with a fixed point of inflection) for describing the relationship between live weight and age are recommended for the following reasons: they are easy to fit, they very often give a closer fit to data points because of their flexibility and therefore a smaller RSS value, than the simpler models, and they encompasses simpler models for the addition of an extra parameter, which is especially important when the behavior of a particular data set is not defined previously.

Time patterns in UK demand for alcohol and tobacco: an application of the EM algorithm

Capturing the pattern of structural change is a relevant task in applied demand analysis, as consumer preferences may vary significantly over time. Filtering and smoothing techniques have recently played an increasingly relevant role. A dynamic Almost Ideal Demand System with random walk parameters is estimated in order to detect modifications in consumer habits and preferences, as well as changes in the behavioural response to prices and income. Systemwise estimation, consistent with the underlying constraints from economic theory, is achieved through the EM algorithm. The proposed model is applied to UK aggregate consumption of alcohol and tobacco, using quarterly data from 1963 to 2003. Increased alcohol consumption is explained by a preference shift, addictive behaviour and a lower price elasticity. The dynamic and time-varying specification is consistent with the theoretical requirements imposed at each sample point. (c) 2005 Elsevier B.V. All rights reserved.

Deconvolution method for removing the distortion from time jitter in equivalent-time waveform samplers

A sampling oscilloscope is one of the main units in automatic pulse measurement system (APMS). The time jitter in waveform samplers is an important error source that affect the precision of data acquisition. In this paper, this kind of error is greatly reduced by using the deconvolution method. First, the probability density function (PDF) of time jitter distribution is determined by the statistical approach, then, this PDF is used as convolution kern to deconvolve with the acquired waveform data with additional averaging, and the result is the waveform data in which the effect of time jitter has been removed, and the measurement precision of APMS is greatly improved. In addition, some computer simulations are given which prove the success of the method given in this paper.