Threshold Autoregressive Model for a Time Series Data

In this paper we try to fit a threshold autoregressive (TAR) model to time series data of monthly coconut oil prices at Cochin market. The procedure proposed by Tsay [7] for fitting the TAR model is briefly presented. The fitted model is compared with a simple autoregressive (AR) model. The results are in favour of TAR process. Thus the monthly coconut oil prices exhibit a type of non-linearity which can be accounted for by a threshold model.

Product autoregressive models for non-negative variables

When variables in time series context are non-negative, such as for volatility, survival time or wave heights, a multiplicative autoregressive model of the type Xt = Xα t−1Vt , 0 ≤ α < 1, t = 1, 2, . . . may give the preferred dependent structure. In this paper, we study the properties of such models and propose methods for parameter estimation. Explicit solutions of the model are obtained in the case of gamma marginal distribution

Analysis of Stochastic Volatility Sequences Generated by Product Autoregressive Models

The classical methods of analysing time series by Box-Jenkins approach assume that the observed series uctuates around changing levels with constant variance. That is, the time series is assumed to be of homoscedastic nature. However, the nancial time series exhibits the presence of heteroscedasticity in the sense that, it possesses non-constant conditional variance given the past observations. So, the analysis of nancial time series, requires the modelling of such variances, which may depend on some time dependent factors or its own past values. This lead to introduction of several classes of models to study the behaviour of nancial time series. See Taylor (1986), Tsay (2005), Rachev et al. (2007). The class of models, used to describe the evolution of conditional variances is referred to as stochastic volatility modelsThe stochastic models available to analyse the conditional variances, are based on either normal or log-normal distributions. One of the objectives of the present study is to explore the possibility of employing some non-Gaussian distributions to model the volatility sequences and then study the behaviour of the resulting return series. This lead us to work on the related problem of statistical inference, which is the main contribution of the thesis

Modelling and Analysis of Some Time Series

The thesis deals with some of the non-linear Gaussian and non-Gaussian time models and mainly concentrated in studying the properties and application of a first order autoregressive process with Cauchy marginal distribution. In this thesis some of the non-linear Gaussian and non-Gaussian time series models and mainly concentrated in studying the properties and application of a order autoregressive process with Cauchy marginal distribution. Time series relating to prices, consumptions, money in circulation, bank deposits and bank clearing, sales and profit in a departmental store, national income and foreign exchange reserves, prices and dividend of shares in a stock exchange etc. are examples of economic and business time series. The thesis discuses the application of a threshold autoregressive(TAR) model, try to fit this model to a time series data. Another important non-linear model is the ARCH model, and the third model is the TARCH model. The main objective here is to identify an appropriate model to a given set of data. The data considered are the daily coconut oil prices for a period of three years. Since it is a price data the consecutive prices may not be independent and hence a time series based model is more appropriate. In this study the properties like ergodicity, mixing property and time reversibility and also various estimation procedures used to estimate the unknown parameters of the process.

Brain Glutamate Dehydrogenase Changes In Streptozotocin Diabetic Rats As A Function Of Age

Kinetic parameters of brain glutamate dehydrogenase (GDH) were compared in the brain stem, cerebellum and cerebral cortex of three weeks and one year old streptozotocin (STZ) induced four day diabetic rats with respective controls. A single intrafemoral dose of STZ (60mg/Kg body weight) was administered to induce diabetes in both age groups. After four days the blood glucose levels showed a significant increase in the diabetic animals of both age groups compared with the respective controls. The increase in blood glucose was significant in one year old compared to the three weeks old diabetic rats. The Vmm of the enzyme was decreased in all the brain regions studied, of the three weeks old diabetic rats without any significant change in the Km. In the adult the Vmax of GDH was increased in cerebellum and brain stem but was unchanged in the cerebral cortex. The K. was unchanged in cerebellum and cerebral cortex but was increased in the brain stem. These results suggest there may be an important regulatory role of the glutamate pathway in brain neural network disturbances and neuronal degeneration in diabetes as a function of age.

Bivariate semi-Pareto distributions and processes

A bivariate semi-Pareto distribution is introduced and characterized using geometric minimization. Autoregressive minification models for bivariate random vectors with bivariate semi-Pareto and bivariate Pareto distributions are also discussed. Multivariate generalizations of the distributions and the processes are briefly indicated.

Gamma stochastic volatility models

This paper presents gamma stochastic volatility models and investigates its distributional and time series properties. The parameter estimators obtained by the method of moments are shown analytically to be consistent and asymptotically normal. The simulation results indicate that the estimators behave well. The insample analysis shows that return models with gamma autoregressive stochastic volatility processes capture the leptokurtic nature of return distributions and the slowly decaying autocorrelation functions of squared stock index returns for the USA and UK. In comparison with GARCH and EGARCH models, the gamma autoregressive model picks up the persistence in volatility for the US and UK index returns but not the volatility persistence for the Canadian and Japanese index returns. The out-of-sample analysis indicates that the gamma autoregressive model has a superior volatility forecasting performance compared to GARCH and EGARCH models.

Estimation for the semipareto processes

This paper proposes different estimators for the parameters of SemiPareto and Pareto autoregressive minification processes The asymptotic properties of the estimators are established by showing that the SemiPareto process is α-mixing. Asymptotic variances of different moment and maximum likelihood estimators are compared.

Hydrogeochemical evaluation of inorganics and bioorganics in selected aquatic environments

The present study is an investigation to address relevant chemical aspects of the three varied aquatic environments, such as mangroves, river and the estuary. The sampling locations include a thick mangrove forest with high tidal activity, a mangrove nursery with minimal disturbances and low tidal inundation, a highly polluted riverine system and an estuarine site, as reference. Nutrients and bioorganic compounds in the water column and surface sediment were estimated in an attempt to understand the regeneration properties of these different aquatic systems.Assessment of the trace metal pollution was also carried out.

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.

Studies on the Effects of Bottom Trawling on the Benthic Fauna off Veraval Coast, Gujarat

Bottom trawling is one among the most destructive human induced physical disturbances inflicted to seabed and its living communities. The bottom trawls are designed to tow along the sea floor, which on its operation indiscriminately smashes everything on their way crushing, killing, burying and exposing to predators the benthic fauna. Bottom trawling causes physical and biological damages that are irreversible, extensive and long lasting. The commercial trawling fleet of India consists of 29,241 small and medium-fishing boats. The northwest coast of India has the largest fishing fleet consisting of 23,618 mechanized vessels, especially the bottom trawlers. However, attempts were not made to study the impact of bottom trawling along Northwest coast of India. The estimated optimum fleet size of Gujarat is 1,473 mechanised trawlers while 7402 commercial trawlers are operated from the coast of Gujarat. Veraval port was designed initially for 1,200 fishing trawlers but 2793 trawlers are being operated from this port making it the largest trawler port of Gujarat. The aim of this study was to investigate the effects of bottom trawling on the substratum and the associated benthic communities of commercial trawling grounds of Veraval coast. The study compared the differences between the samples collected before and after experimental trawling to detect the impacts of bottom trawling. Attempts were made to assess the possible impact of bottom trawling on:(i) the sediment characteristics (ii)the sediment heavy metals (iii) epifauna (iv) macrobenthos and (v) meiobenthos. This study is expected to generate information on trawling impacts of the studied area that will help in better management of the biological diversity and integrity of the benthic fauna off Veraval coast. An exhaustive review on the studies conducted around the world and in India on impact of bottom trawling on the benthic fauna is also detailed.In the present study, the bottom trawling induced variations on sediment organic matter, epifauna, macrobenthos and meiobenthos were evident. It was also observed that the seasonal/ natural variations were more prominent masking the trawling effect on sediment texture and heavy metals. Enforcement of control of excess bottom trawlers and popularization of semi pelagic trawls designed to operate a little distance above the sea bottom for off bottom resources will minimize disturbance on the sea bottom. Training and creating awareness in responsible fishing should be made mandatory requirements, to the coastal communities. They should be made wardens to protect the valuable resources for the benefit of sustainability. To protect the biodiversity and ecosystem health, the imminent need is to survey and make catalogue, identification of sensitive areas or hot spots and to adopt management strategies for the conservation and biodiversity protection of benthic fauna. The present study is a pioneering work carried out along Veraval coast. This thesis will provide a major fillip to the studies on impact of bottom trawling on the benthic fauna along the coast of India.

Biochemical Studies on the Protective Effect of Taurine on Experimentally Induced Fulminat Hepatic Failure in Rats

Fulminant hepatic failure (FHF) is a dramatic and challenging syndrome in clinical medicine. Although an uncommon disorder, it is usually fatal and occurs in previously healthy person. While the causes of FHF remain unclear, viral hepatitis and drug-induced liver injury account for the majority of cases. Hepatitis E causes large-scale epidemics of hepatitis in the Indian subcontinent, involving hundreds of thousands of cases with high mortality. FHF is associated with several clinical features like jaundice, shrunken liver, easy bruising, low levels of serum proteins, fatigue, multi-organ failure etc and metabolic derangements like hypoglycemia, hyperlipidemia, hyponatremia, defective protein synthesis, reduced energy production, decreased rate of urea production etc. These disturbances are predominantly attributed to oxidative stress, membrane destabilization and osmolytic imbalances. The options available for these patients are quite minimal with liver transplantation being one of them. But the procedure is ridden with issues causing it to find less favor among the patients and the caregivers. Use of hepatoprotective and cytoprotective drugs, is being considered to be a more acceptable alternative as a strategy to enhance liver regeneration. In this regard use of taurine a naturally occurring amino acid that plays a crucial role in many physiological processes would prove to be effective. In the present study, hepatoprotective effect of taurine on a rat model of induced FHF was studied. Taurine supplementation has effectively counteracted the metabolic and structural aberrations in the liver caused by D-galactosamine intoxication.

Seasonal and interannual variability of sea level and associated surface meteorological parameters at Cochin

This thesis entitled seasonal and interannual variability of sea level and associated surface meteorological parameters at cochin.The interesting aspect of studying sea level variability on different time scales can be attributed to the diversity of its applications.Study of tides could perhaps be the oldest branch of physical oceanography.The thesis is presented in seven chapters. The first chapter gives, apart from a general introduction, a survey of literature on sea level variability on different time scales - tidal, seasonal and interannual (geological scales excluded), with particular emphasis on the work carried out in the Indian waters. The second chapter is devoted to the study of observed tides at Cochin on seasonal and interannual time scales using hourly water level data for the period 1988-1993. The third chapter describes the long-term climatology of some important surface oceanographic and meteorological parameters (at Cochin) which are supposed to affect the sea level. The fourth chapter addresses the problem of seasonal forecasting of the meteorological and oceanographic parameters at Cochin using autoregressive, sinusoidal and exponentially weighted moving average techniques and testing their accuracy with the observed data for the period 1991-1993. The fifth chapter describes the seasonal cycles of sea level and the driving forces at 16 stations along the Indian subcontinent. It also addresses the observed interannual variability of sea level at 15 stations using available multi-annual data sets. The sixth chapter deals with the problem of coastal trapped waves between Cochin and Beypore off the Kerala coast using sea level and atmospheric pressure data sets for the year 1977. The seventh and the last chapter contains the summary and conclusions and future outlook based on this study.

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.