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.

‘Systematics and pathogenicity of Vibrionaceae associated T ¢ S with the larvae of M. rosenbergii in hatchery

Even though Bergey '5 Manual has been recognized globally as the guide to bacterial systematics, it has to be emphasized that descriptions given to a large extent are based on studies made with temperate isolates This leads one to conclude that any attempt to identify the tropical isolates with identification keys and tables generated from this information may lead to erroneous conclusions. And there is every possibility of the existence of genotypic and phenotypic variants or even nev. species in this part ofthe aquatic ecosystem. Applications ofa polythetic scheme of classification based on the principles of Numerical Taxonomy opens up exciting avenues for bringing to light, this possibility which otherwise would have been masked by the unidirectional approach as in monothetic schemes. Another added advantage of clustering a ‘natural’ bacterial population by numerical taxonomy, is the ease by which genotypic characterization could be performed on the clusters by selecting a representative from each cluster This helps overcome the practical impossibility of analyzing all the isolates in a pani:'_lar cluster. The genotypic characteizarion would either be mole °/o G-'rC. DNA-D.\_-X hybridization, DNA-RNA hybridization or DNA fingerprinting. Considering the requirement creating a broad base in the understanding of the family Vibrionaceae associated with the larvae ofM rosenbergii, the present work was undertaken to channelize every new information generated for developing appropriate managerial measures to protect the larvae from vibriosis during the unusually prolonged larval phase.

“Studies on the Biology, Morphometrics and Biochemical composition of the Ommastrephid squid, Sthenoteuthis oualaniensis (Lesson,1830) of the south west coast of India”

With the stabilization of world finfish catches in general, and the depletion of a number of fish stocks that used to support industrial-scale fisheries, increasing attention is now being paid, to the so-called unconventional marine resources, which include many species of cephalopods. One of such important cephalopod resource is the tropical Indo-Pacific pelagic oceanic squid Sthenoteuthis oualaniensis. It is the most abundant large sized squid in the Indo- Pacific region with an estimated biomass of 8-11 metric tons. However, its distribution, biology, life cycle and nutrient value in the south west coast of India are still poorly known. So any new information of this species in the waters off the south west coast of India has important scientific significance for effective and rational utilization of this Oceanic fishery resources, especially during the time of depletion of shallow water resources. In view of that this study investigated different aspects of the Sthenoteuthis oualaniensis, such as morphometry, growth, mortality, maturation, spawning, food, feeding and biochemical composition in the south west coast of India to understand its possible prospective importance for commercial fishing and management of its fishery

Performance analysis of FIR digital filter design: RNS versus traditional

Residue Number System (RNS) based Finite Impulse Response (FIR) digital filters and traditional FIR filters. This research is motivated by the importance of an efficient filter implementation for digital signal processing. The comparison is done in terms of speed and area requirement for various filter specifications. RNS based FIR filters operate more than three times faster and consumes only about 60% of the area than traditional filter when number of filter taps is more than 32. The area for RNS filter is increasing at a lesser rate than that for traditional resulting in lower power consumption. RNS is a nonweighted number system without carry propogation between different residue digits.This enables simultaneous parallel processing on all the digits resulting in high speed addition and multiplication in the RNS domain

Prediction of Learning Disabilities in School Age Children using SVM and Decision Tree

This paper highlights the prediction of Learning Disabilities (LD) in school-age children using two classification methods, Support Vector Machine (SVM) and Decision Tree (DT), with an emphasis on applications of data mining. About 10% of children enrolled in school have a learning disability. Learning disability prediction in school age children is a very complicated task because it tends to be identified in elementary school where there is no one sign to be identified. By using any of the two classification methods, SVM and DT, we can easily and accurately predict LD in any child. Also, we can determine the merits and demerits of these two classifiers and the best one can be selected for the use in the relevant field. In this study, Sequential Minimal Optimization (SMO) algorithm is used in performing SVM and J48 algorithm is used in constructing decision trees.