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

Box Products in Fuzzy Topological Spaces and Related Topics

The topology as the product set with a base chosen as all products of open sets in the individual spaces. This topology is known as box topology. The main objective of this study is to extend the concept of box products to fuzzy box products and to obtain some results regarding them. Owing to the fact that box products have plenty of applications in uniform and covering properties, here made an attempt to explore some inter relations of fuzzy uniform properties and fuzzy covering properties in fuzzy box products. Even though the main focus is on fuzzy box products, some brief sketches regarding hereditarily fuzzy normal spaces and fuzzy nabla product is also provided. The main results obtained include characterization of fuzzy Hausdroffness and fuzzy regularity of box products of fuzzy topological spaces. The investigation of the completeness of fuzzy uniformities in fuzzy box products proved that a fuzzy box product of spaces is fuzzy topologically complete if each co-ordinate space is fuzzy topologically complete. The thesis also prove that the fuzzy box product of a family of fuzzy α-paracompact spaces is fuzzy topologically complete. In Fuzzy box product of hereditarily fuzzy normal spaces, the main result obtained is that if a fuzzy box product of spaces is hereditarily fuzzy normal ,then every countable subset of it is fuzzy closed. It also deals with the notion of fuzzy nabla product of spaces which is a quotient of fuzzy box product. Here the study deals the relation connecting fuzzy box product and fuzzy nabla product

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.

Influence Of Forecasting, Planning And Controlling On The Performance Of Small And Medium Enterprises

Production Planning and Control (PPC) systems have grown and changed because of the developments in planning tools and models as well as the use of computers and information systems in this area. Though so much is available in research journals, practice of PPC is lagging behind and does not use much from published research. The practices of PPC in SMEs lag behind because of many reasons, which need to be explored This research work deals with the effect of identified variables such as forecasting, planning and control methods adopted, demographics of the key person, standardization practices followed, effect of training, learning and IT usage on firm performance. A model and framework has been developed based on literature. Empirical testing of the model has been done after collecting data using a questionnaire schedule administered among the selected respondents from Small and Medium Enterprises (SMEs) in India. Final data included 382 responses. Hypotheses linking SME performance with the use of forecasting, planning and controlling were formed and tested. Exploratory factor analysis was used for data reduction and for identifying the factor structure. High and low performing firms were classified using a Logistic Regression model. A confirmatory factor analysis was used to study the structural relationship between firm performance and dependent variables.

Assessment of Energy Conservation in Indian Cement Industry and Forecasting of Co2 Emissions

Cement industry ranks 2nd in energy consumption among the industries in India. It is one of the major emitter of CO2, due to combustion of fossil fuel and calcination process. As the huge amount of CO2 emissions cause severe environment problems, the efficient and effective utilization of energy is a major concern in Indian cement industry. The main objective of the research work is to assess the energy cosumption and energy conservation of the Indian cement industry and to predict future trends in cement production and reduction of CO2 emissions. In order to achieve this objective, a detailed energy and exergy analysis of a typical cement plant in Kerala was carried out. The data on fuel usage, electricity consumption, amount of clinker and cement production were also collected from a few selected cement industries in India for the period 2001 - 2010 and the CO2 emissions were estimated. A complete decomposition method was used for the analysis of change in CO2 emissions during the period 2001 - 2010 by categorising the cement industries according to the specific thermal energy consumption. A basic forecasting model for the cement production trend was developed by using the system dynamic approach and the model was validated with the data collected from the selected cement industries. The cement production and CO2 emissions from the industries were also predicted with the base year as 2010. The sensitivity analysis of the forecasting model was conducted and found satisfactory. The model was then modified for the total cement production in India to predict the cement production and CO2 emissions for the next 21 years under three different scenarios. The parmeters that influence CO2 emissions like population and GDP growth rate, demand of cement and its production, clinker consumption and energy utilization are incorporated in these scenarios. The existing growth rate of the population and cement production in the year 2010 were used in the baseline scenario. In the scenario-1 (S1) the growth rate of population was assumed to be gradually decreasing and finally reach zero by the year 2030, while in scenario-2 (S2) a faster decline in the growth rate was assumed such that zero growth rate is achieved in the year 2020. The mitigation strategiesfor the reduction of CO2 emissions from the cement production were identified and analyzed in the energy management scenarioThe energy and exergy analysis of the raw mill of the cement plant revealed that the exergy utilization was worse than energy utilization. The energy analysis of the kiln system showed that around 38% of heat energy is wasted through exhaust gases of the preheater and cooler of the kiln sysetm. This could be recovered by the waste heat recovery system. A secondary insulation shell was also recommended for the kiln in the plant in order to prevent heat loss and enhance the efficiency of the plant. The decomposition analysis of the change in CO2 emissions during 2001- 2010 showed that the activity effect was the main factor for CO2 emissions for the cement industries since it is directly dependent on economic growth of the country. The forecasting model showed that 15.22% and 29.44% of CO2 emissions reduction can be achieved by the year 2030 in scenario- (S1) and scenario-2 (S2) respectively. In analysing the energy management scenario, it was assumed that 25% of electrical energy supply to the cement plants is replaced by renewable energy. The analysis revealed that the recovery of waste heat and the use of renewable energy could lead to decline in CO2 emissions 7.1% for baseline scenario, 10.9 % in scenario-1 (S1) and 11.16% in scenario-2 (S2) in 2030. The combined scenario considering population stabilization by the year 2020, 25% of contribution from renewable energy sources of the cement industry and 38% thermal energy from the waste heat streams shows that CO2 emissions from Indian cement industry could be reduced by nearly 37% in the year 2030. This would reduce a substantial level of greenhouse gas load to the environment. The cement industry will remain one of the critical sectors for India to meet its CO2 emissions reduction target. India’s cement production will continue to grow in the near future due to its GDP growth. The control of population, improvement in plant efficiency and use of renewable energy are the important options for the mitigation of CO2 emissions from Indian cement industries