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

Production of Alkaline Protease by Free and Immobilised Cells of VIBRIO sp. Under Different Fermentation Systems and Its Application on Deproteinisation of Prawn Shell Waste for Chitin Recovery

This thesis presents a detailed account of a cost - effective approach towards enhanced production of alkaline protease at profitable levels using different fermentation designs employing cheap agro-industrial residues. It involves the optimisation of process parameters for the production of a thermostable alkaline protease by Vibrio sp. V26 under solid state, submerged and biphasic fermentations, production of the enzyme using cell immobilisation technology and the application of the crude enzyme on the deproteinisation of crustacean waste.The present investigation suggests an economic move towards Improved production of alkaline protease at gainful altitudes employing different fermentation designs utilising inexpensive agro-industrial residues. Moreover, the use of agro-industrial and other solid waste substrates for fermentation helps to provide a substitute in conserving the already dwindling global energy resources. Another alternative for accomplishing economically feasible production is by the use of immobilisation technique. This method avoids the wasteful expense of continually growing microorganisms. The high protease producing potential of the organism under study ascertains their exploitation in the utilisation and management of wastes. However, strain improvement studies for the production of high yielding variants using mutagens or by gene transfer are required before recommending them to Industries.Industries, all over the world, have made several attempts to exploit the microbial diversity of this planet. For sustainable development, it is essential to discover, develop and defend this natural prosperity. The Industrial development of any country is critically dependent on the intellectual and financial investment in this area. The need of the hour is to harness the beneficial uses of microbes for maximum utilisation of natural resources and technological yields. Owing to the multitude of applications in a variety of industrial sectors, there has always been an increasing demand for novel producers and resources of alkaline proteases as well as for innovative methods of production at a commercial altitude. This investigation forms a humble endeavour towards this perspective and bequeaths hope and inspiration for inventions to follow.

Dopamine Receptor Subtypes,IP3, cAMP and cGMP Functional Regulation in Parkinsonism Induced by Unilateral Infusion of Rotenone in Rats: Recovery with Bone Marrow Cells,Serotonin and GABA Supplementation

In the present study, the effects of 5-HT, GABA and Bone Marrow Cells infused intranigrally to substantia nigra individually and in combinations on unilateral rotenone infused Parkinsonism induced rats. Scatchard analysis of DA, DA D1 and D2 receptors in the corpus striatum, cerebral cortex, cerebellum, brain stem and hippocampus showed a significant increase in the Brain regions of rotenone infused rat compared to control. Real Time PCR amplification of DA D1, D2, Bax and ubiquitin carboxy-terminal hydrolase were up regulated in the brain regions of rotenone infused rats compared to control. Gene expression studies of -Synuclien, cGMP and Cyclic AMP response element-binding protein showed a significant down regulation in Rotenone infused rats compared to control. Behavioural studies were carried out to confirm the biochemical and molecular studies.Our study demonstrated that BMC administration alone cannot reverse the above said molecular changes occurring in PD rat. 5-HT and GABA acting through their specific receptors in combination with bone marrow cells play a crucial role in the functional recovery of PD rats. 5-HT, GABA and Bone marrow cells treated PD rats showed significant reversal to control in DA receptor binding and gene expression. 5-HT and GABA have co-mitogenic property. Proliferation and differentiation of cells re-establishing the connections in Parkinson's disease facilitates the functional recovery. Thus, it is evident that 5-HT and GABA along with BMC to rotenone infused rats renders protection against oxidative, related motor and cognitive deficits which makes them clinically significant for cellbased therapy. The BMC transformed to neurons when co-transplanted with 5-HT and GABA which was confirmed with PKH2GL and nestin. These newly formed neurons have functional significance in the therapeutic recovery of Parkinson’s disease.