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.

Modelling and Analysis of Recurrent Event Data with Multiple Causes

This thesis Entitled “modelling and analysis of recurrent event data with multiple causes.Survival data is a term used for describing data that measures the time to occurrence of an event.In survival studies, the time to occurrence of an event is generally referred to as lifetime.Recurrent event data are commonly encountered in longitudinal studies when individuals are followed to observe the repeated occurrences of certain events. In many practical situations, individuals under study are exposed to the failure due to more than one causes and the eventual failure can be attributed to exactly one of these causes.The proposed model was useful in real life situations to study the effect of covariates on recurrences of certain events due to different causes.In Chapter 3, an additive hazards model for gap time distributions of recurrent event data with multiple causes was introduced. The parameter estimation and asymptotic properties were discussed .In Chapter 4, a shared frailty model for the analysis of bivariate competing risks data was presented and the estimation procedures for shared gamma frailty model, without covariates and with covariates, using EM algorithm were discussed. In Chapter 6, two nonparametric estimators for bivariate survivor function of paired recurrent event data were developed. The asymptotic properties of the estimators were studied. The proposed estimators were applied to a real life data set. Simulation studies were carried out to find the efficiency of the proposed estimators.

Studies on the structural, electrical and magnetic properties of composites based on spinel ferrites

This thesis mainly deals with the preparation and studies on magnetic composites based on spinel ferrites prepared both chemically and mechanically. Rubber ferrite composites (RFC) are chosen because of their mouldability and flexibility and the ease with which the dielectric and magnetic properties can be manipulated to make them as useful devices. Natural rubber is chosen as the Matrix because of its local availability and possible value addition. Moreover, NR represents a typical unsaturated nonpolar matrix. The work can be thought of as two parts. Part l concentrates on the preparation and characterization of nanocomposites based on y-Fe203. Part 2 deals with the preparation and characterization of RFCs containing Nickel zinc ferrit In the present study magnetic nanocomposites have been prepared by ionexchange method and the preparation conditions have been optimized. The insitu incorporation of the magnetic component is carried out chemically. This method is selected as it is the easiest and simplest method for preparation of nanocomposite. Nanocomposite samples thus prepared were studied using VSM, Mossbauer spectroscopy, Iron content estimation, and ESR spectroscopy. For the preparation of RFCs, the filler material namely nickel zinc ferrite having the general formula Ni)_xZnxFez04, where x varies from 0 to 1 in steps of 0.2 have been prepared by the conventional ceramic techniques. The system of Nil_xZn"Fe204 is chosen because of their excellent high frequency characteristics. After characterization they are incorporated into the polymer matrix of natural rubber by mechanical method. The incorporation is done according to a specific recipe and for various Loadings of magnetic fillers and also for all compositions. The cure characteristics, magnetic properties and dielectric properties of these composites are evaluated. The ac electrical conductivity of both ceramic nickel zinc ferrites and rubber ferrite composites are also calculated using a simple relation. The results are correlated.

“Effects of monospecific and mixed algal diets on survival, development and biochemical composition of Penaeus monodon larvae”

The main objective of the present work is to acquire information regarding the growth responses of P. monodon larvae (from PZ1 upto PL1) to various mono specific and mixed diets. Evaluate the nutritional quality of selected species of micro algae viz. Chaetoceros calcitrans, Dunaliella salina, Isochrysis galbana and Nannochloropsis salina, larvae at three cell concentrations 10x104 cells/ml, 25x104 cells/ml and 50x104 cells/ml. The P. monodon larvae were transported, at the Nauplius stage, to the laboratory. The larvae were stocked at density of 150 larvae per litre in 5 litre FRP tanks with 3 litres of sea water. The algal cell density given to the larvae varied. The larval stages were fed with increasing densities of algae to evaluate the relationship between the food densities, ingestion rates, development and growth of the larvae. The water quality parameters, the percentage of survival rate, the growth estimation and the algal cell count were done. Each experiment was carried out in triplicate with a control group of larvae fed with Chaetoceros calcitrans. For the estimation standard procedures were used.to P. monodon