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.

A Diagnostic and Modeling Study on the Onset of Summer Monsoon over South Asia

This study focuses on the onset of southwest monsoon over Kerala. India Meteorological Department (IMD) has been using a semi-objective method to define monsoon onset. The main objectives of the study are to understand the monsoon onset processes, to simulate monsoon onset in a GCM using as input the atmospheric conditions and Sea Surface Temperature, 10 days earlier to the onset, to develop a method for medium range prediction of the date of onset of southwest monsoon over Kerala and to examine the possibility of objectively defining the date of Monsoon Onset over Kerala (MOK). It gives a broad description of regional monsoon systems and monsoon onsets over Asia and Australia. Asian monsoon includes two separate subsystems, Indain monsoon and East Asian monsoon. It is seen from this study that the duration of the different phases of the onset process are dependent on the period of ISO. Based on the study of the monsoon onset process, modeling studies can be done for better understanding of the ocean-atmosphere interaction especially those associated with the warm pool in the Bay of Bengal and the Arabian Sea.

Modeling of Suspended Sediment Dynamics in Tropical River Basins

It is proposed to study the suspended sediment transport characteristics of river basins of Kerala and to model suspended sediment discharge mechanism for typical micro-watersheds. The Pamba river basin is selected as a representative hydrologic regime for detailed studies of suspended sediment characteristics and its seasonal variation. The applicability of various erosion models would be tested by comparing with the observed event data (by continuous monitoring of rainfall, discharge, and suspended sediment concentration for lower order streams). Empirical, conceptual and physically distributed models were used for making the comparison of performance of the models. Large variations in the discharge and sediment quantities were noticed during a particular year between the river basins investigated and for an individual river basin during the years for which the data was available. In general, the sediment yield pattern follows the seasonal distribution of rainfall, discharge and physiography of the land. This confirms with similar studies made for other Indian rivers. It was observed from this study, that the quantity of sediment transported downstream shows a decreasing trend over the years corresponding to increase in discharge. For sound and sustainable management of coastal zones, it is important to understand the balance between erosion and retention and to quantify the exact amount of the sediments reaching this eco-system. This, of course, necessitates a good length of time series data and more focused research on the behaviour of each river system, both present and past. In this realm of river inputs to ocean system, each of the 41 rivers of Kerala may have dominant yet diversified roles to influence the coastal ecosystem as reflected from this study on the major fraction of transport, namely the suspended sediments

A Comaparison Study of EM and Physical Equivalent Circuit Modeling for MIM CMOS Capacitors

In this Letter a new physical model for metal-insulatormetal CMOS capacitors is presented. In the model the parameters of the circuit are derived from the physical structural details. Physical behaviors due to metal skin effect and inductance have been considered. The model has been confirmed by 3D EM simulator and design rules proposed. The model presented is scalable with capacitor geometry, allowing designers to predict and optimize quality factor. The approach has been verified for MIM CMOS capacitors

Direction Dependent Transmission Characteristics of Dye Mixture Doped Polymer Optical Fibre Preforms

The direction dependant wavelength selective transmission mechanism in poly (methyl methacrylate)(PMMA) rods doped with C 540 dye and C 540:Rh.B dye mixture as a combination has been investigated. When a polished slice of pure C 540 doped polymer rod was used side by side with a C540:Rh B doped rod with acceptor concentration [A] = 7x10-4 m/l , we could notice more than 100% change in the transmitted intensity along opposite directions at the C 540, Rh B emission and the excitation wavelengths . A blue high bright LED emitting at a peak wavelength 465nm was used as the excitation source.

Direction Dependent Transmission Characteristics of Dye Mixture Doped Polymer Optical Fibre Preforms

The direction dependant wavelength selective transmission mechanism in poly (methyl methacrylate)(PMMA) rods doped with C 540 dye and C 540:Rh.B dye mixture as a combination has been investigated. When a polished slice of pure C 540 doped polymer rod was used side by side with a C540:Rh B doped rod with acceptor concentration [A] = 7x10-4 m/l , we could notice more than 100% change in the transmitted intensity along opposite directions at the C 540, Rh B emission and the excitation wavelengths . A blue high bright LED emitting at a peak wavelength 465nm was used as the excitation source.

Direction Dependent Transmission Characteristics of Dye Mixture Doped Polymer Optical Fibre Preforms

The direction dependant wavelength selective transmission mechanism in poly (methyl methacrylate)(PMMA) rods doped with C 540 dye and C 540:Rh.B dye mixture as a combination has been investigated. When a polished slice of pure C 540 doped polymer rod was used side by side with a C540:Rh B doped rod with acceptor concentration [A] = 7x10-4 m/l , we could notice more than 100% change in the transmitted intensity along opposite directions at the C 540, Rh B emission and the excitation wavelengths . A blue high bright LED emitting at a peak wavelength 465nm was used as the excitation source.

Excitation wavelength dependence of energy transfer in dye mixture doped polymer optical fibre preforms

Dependence of energy transfer parameters on excitation wavelength has been investigated in poly (methyl methacrylate) (PMMA) optical fibre preforms doped with C 540:Rh B dye mixture by studying the fluorescence intensity and the lifetime variations. A fluorescence spectrophotometer was used to record the excitation spectra of the samples for the emission wavelengths 495 and 580 nm. The fluorescence emission from the polymer rods was studied at four specific excitation wavelengths viz; 445, 465, 488 and 532 nm. The fluorescence lifetime of the donor molecule was experimentally measured in polymer matrix by time correlated single photon counting technique. The energy transfer rate constants and transfer efficiencies were calculated and their dependence on the acceptor concentration was analysed for three excitation wavelengths. It was found that any change in the excitation wavelength leads to significant variations in the quenching characteristics, which in turn affect the calculated energy transfer parameters.

Fabrication and characterization of dye mixture doped polymer optical fiber as a broad wavelength optical amplifier

Rhodamine 6G and Rhodamine B dye mixture doped polymer optical fiber amplifier (POFA), which can operate in a broad wavelength region (60 nm), has been successfully fabricated and tested. Tunable operation of the amplifier over a broad wavelength region is achieved by mixing different ratios of the dyes. The dye doped POFA is pumped axially using 532 nm, 10 ns laser pulses from a frequency doubled Q-switched Nd: YAG laser and the signals are taken from an optical parametric oscillator. A maximum gain of 22.3 dB at 617 nm wavelength has been obtained for a 7 cm long dye mixture doped POFA. The effects of pump energy and length of the fiber on the performance of the fiber amplifier are also studied. There exists an optimum length for which the amplifier gain is at a maximum value.

Photoacoustic study on the photostability of polymethyl methacrylate films doped with Rhodamine 6G–Rhodamine B dye mixture system

The photosensitivity of dye mixture-doped polymethyl methacrylate (PMMA) films are investigated as a function of laser power, concentration of the dyes, modulation frequency and the irradiation wavelength. Energy transfer from a donor molecule to an acceptor molecule affects the emission output of the dye mixture system. Photosensitivity is found to change with changes in donor–acceptor concentrations. PMMA samples doped with the dye mixture are found to be more photosensitive when the dyes are mixed in the same proportion.

Income modeling using Quantile Functions

Department of Statistics, Cochin University of Science and Technology

On Finite Mixture of Pareto and Beta Distnbutions

Department of Statistics, Cochin University of Science and Technology

Nitrifying Bioreactors Integrated into Shrimp and Prawn Hatchery Systems: Molecular Characterization of the Nitrifying Consortia,Reactor Kinetics, Modeling and Validation

National Centre for Aquatic Animal Health, Cochin University of Science and Technology

Tropical Mesoscale Convective Systems and Associated Energetics : Observational and Modeling Studies

The main purpose of the thesis is to improve the state of knowledge and understanding of the physical structure of the TMCS and its short range prediction. The present study principally addresses the fine structure, dynamics and microphysics of severe convective storms.The structure and dynamics of the Tropical cloud clusters over Indian region is not well understood. The observational cases discussed in the thesis are limited to the temperature and humidity observations. We propose a mesoscale observational network along with all the available Doppler radars and other conventional and non—conventional observations. Simultaneous observations with DWR, VHF and UHF radars of the same cloud system will provide new insight into the dynamics and microphysics of the clouds. More cases have to be studied in detail to obtain climatology of the storm type passing over tropical Indian region. These observational data sets provide wide variety of information to be assimilated to the mesoscale data assimilation system and can be used to force CSRM.The gravity wave generation and stratosphere troposphere exchange (STE) processes associated with convection gained a great deal of attention to modem science and meteorologist. Round the clock observations using VHF and UHF radars along with supplementary data sets like DWR, satellite, GPS/Radiosondes, meteorological rockets and aircrafl observations is needed to explore the role of convection and associated energetics in detail.

ARMA modeling of time series based on rational approximation of spectral density function

This study is concerned with Autoregressive Moving Average (ARMA) models of time series. ARMA models form a subclass of the class of general linear models which represents stationary time series, a phenomenon encountered most often in practice by engineers, scientists and economists. It is always desirable to employ models which use parameters parsimoniously. Parsimony will be achieved by ARMA models because it has only finite number of parameters. Even though the discussion is primarily concerned with stationary time series, later we will take up the case of homogeneous non stationary time series which can be transformed to stationary time series. Time series models, obtained with the help of the present and past data is used for forecasting future values. Physical science as well as social science take benefits of forecasting models. The role of forecasting cuts across all fields of management-—finance, marketing, production, business economics, as also in signal process, communication engineering, chemical processes, electronics etc. This high applicability of time series is the motivation to this study.