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

"Statistical Methods in Gear Selectivity and Gear Efficiency Studies”

The preceding discussion and review of literature show that studies on gear selectivity have received great attention, while gear efficiency studies do not seem to have received equal consideration. In temperate waters, fishing industry is well organised and relatively large and well equipped vessels and gear are used for commercial fishing and the number of species are less; whereas in tropics particularly in India, small scale fishery dominates the scene and the fishery is multispecies operated upon by nmltigear. Therefore many of the problems faced in India may not exist in developed countries. Perhaps this would be the reason for the paucity of literature on the problems in estimation of relative efficiency. Much work has been carried out in estimating relative efficiency (Pycha, 1962; Pope, 1963; Gulland, 1967; Dickson, 1971 and Collins, 1979). The main subject of interest in the present thesis is an investigation into the problems in the comparison of fishing gears. especially in using classical test procedures with special reference to the prevailing fishing practices (that is. with reference to the catch data generated by the existing system). This has been taken up with a view to standardizing an approach for comparing the efficiency of fishing gear. Besides this, the implications of the terms ‘gear efficiency‘ and ‘gear selectivity‘ have been examined and based on the commonly used selectivity model (Holt, 1963), estimation of the ratio of fishing power of two gear has been considered. An attempt to determine the size of fish for which a gear is most efficient.has also been made. The work has been presented in eight chapters