The role of lower partial moments in stochastic modeling

Lower partial moments plays an important role in the analysis of risks and in income/poverty studies. In the present paper, we further investigate its importance in stochastic modeling and prove some characterization theorems arising out of it. We also identify its relationships with other important applied models such as weighted and equilibrium models. Finally, some applications of lower partial moments in poverty studies are also examined

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

Population characteristics and taxonomy of lantern fishes of genus Diaphus (Family Myctophidae) off south west coast of India

Globally most of the conventional fish stocks have reached a state of optimum exploitation or even over-exploitation; efficient utilization of non-conventional resources is necessary to meet the supply-demand gap for protein supply. Mesopelagic fishes can be considered as one such promising resource for the future, if appropriate harvest and post-harvest technologies are developed. Increasing human population and increasing demand for cheaper food fishes has made myctophids a possible potential resource for future exploitation and utilization. Earlier studies indicated the abundance of Diaphus spp. in the eastern and northeastern Arabian Sea. The present study also indicates the dominance of Diaphus spp. in the deep sea trawling grounds of south west coast of India. Commercial viability of the myctophid fishing in the Indian waters has to be worked out. The present catch estimation is based on the Stratified Random Sampling Method from the landing data. As the coverage of sampling area was limited and the gear efficiency was not standardized, the data generated are not precise. A counter check for the estimates is also not possible due to the absence of comparable works in the study area. Fish biomass estimation by acoustics survey coupled with direct fishing would only confirm the accuracy of estimates. Exploratory surveys for new fishing areas to be continued, for gathering the distribution, abundance, biological and ecological data and map the potential fishing ground on a GIS platform and the data should be provided to the commercial entrepreneurs. Generally non-conventional and non-targeted resources are under low fishing pressure and exploitation rates. Low values of fishing mortality and exploitation rates indicate that removal from the stock by fishing was only nominal from the present fishing grounds. The results indicate that the stock is almost at virgin state and remains grossly underexploited. Since the extent of distribution and abundance of the stock in the ecosystem remains to be ascertained, sustainable yield could not be estimated. Also the impact of myctophids harvest, on other commercially important fishes, has to be studied.