The unemployment is one of the main economic indicators. Thanks to time series analysis and predicting values, we can take measures of eliminating negative aspects of the unemployment in the economy. This thesis is concentrated on connection between theory of unemployment with time series analysis of unemployment rate, especially based on Box-Jenkins methodology.

This master thesis is divided into two parts. First part focuses on production and consumption of electricity in the Czech republic, describing sources of the production and their progress since 1990, considering also the main electricity consumers. The end of the first part focuses on the Box-Jenkins methodology, time series of electricity consumption between 1981 and 2008 are created as well as forecasted up to 2011. The second part of this thesis describes the cluster analysis. This is used for finding similarities of the 27 states of the European Union. Cluster analysis is applied for years 1990 and 2007, for both electric power production and electric power consumption.

The aim of this finish work is an analysis of selected demographic time series and calculation of their predictions. Concretely, it deals with time series of annual crude birth rate, crude death rate, and the average age of mothers at first birth, all for the time period of 1960-2013. First, demographic terms used further in the work are defined. There is also a theoretical part describing the statistical methods used, specifically the methodology of time series from authors Box-Jenkins. Developement of each time serie is evaluated socio-demographically and the procedure of selecting the most appropriate interpolation model and calculation of predictions derived from it are described. There is also description of a process of selecting a suitable model based on the extrapolation method of predictions with Rolling Origin, construction of predictions derived from it and their comparison with the most suitable interpolation model. At the end there is a comparison of the time series of crude birth rate between the Czech Republic and selected developed country (Sweden), which brings interesting results.

Indicators of child mortality in the lowest age reflect the status of health care and maturity of the country. The most frequent indicator in this area is the infant mortality rate. This thesis is focused on evaluation of development of infant, neonatal and early neonatal rate in the European union between 1960 and 2010 from the perspective of time series, aplication of Box-Jenkins methodology and assessment of the relation between infant mortality rate and life expectancy at birth.

This thesis is focused on two demographic processes -- nuptiality and divorce rate. The goal of this thesis is to analyze past, present and future development of nuptiality and divorce rate in Czech Republic and to draw a comparison between this development and the development in selected countries of European Union. The evaluation of the past and present development is made by using selected indicators of nuptiality and divorce rate. The forecast of the future development is obtained by using the Box-Jenkins methodology. The comparison of nuptiality and divorce rate in Czech Republic and in selected countries of European Union (Italy, Netherlands, Slovakia, Spain and Sweden) is to be found in the last chapter of this thesis.

The aim of this work is a statistical analysis of expenditures of households on culture, description of current economical situation in the field of cinematography, characteristics of a cinemagoer and a projection of future developmental tendencies of cinemas. The first two chapters are dedicated to a description of the current state of the Czech cinematography and information about the evolution of the Czech film production. The third theoretical part describes basic statistical methods used in the practical part of this work. The fourth part is focused on a film viewer -cinemagoer using MML-TGI method and it also includes analysis of the dependence of expenditures of households for culture on the cinema ticket price. The fifth part is dedicated to a projection of the future development of the attendance and receipts of cinemas. The final chapter deals with the state of European cinematography.

Two real time series, one discussing the area of energy, other discussing the area of economy. By the energetic area we will be dealing with the electric power consumption in the USA, by the economic area we will be dealing with the progress of index PX50. We will try to approve the validity of hypothesis that with some test functions we will be able to set down the accidental unit distribution in these two time series.

The aim of the thesis mainly is to understand an issue of time series analysis. There are many methods in time series analysis, but purpose of this analysis persists the same, which is a construction of sufficient model of time series and his application in forecasting of time series. We have to make a basic identification of time series to establish right process in model constructing. The first and the second chapter is devoted to this basic identification. There are many methods, how we said before, for constructing of concrete model. In this thesis, exactly in the third chapter, we introduce one of the most flexible methodology of model constructing. That is The Box-Jenkins methodology, which was defined in 1976 by these men. In the last chapter we try to put to use insight in the issue of time series analysis for comparison and separation of the space of time series and this comparison use for the right interpretation of the parameters of time series model. The diploma project was supported by project from MSMT of the Czech Republic no. 1M06047 "Centre for Quality and Reliability of Production".

The concise description of one- and multidimensional stationary and non stationary vehicle loading histories for fatigue analysis using stochastic process theory is presented in this study. The load history is considered to have stationary random and nonstationary mean and variance content. The stationary variations are represented by a class of time series referred to as Autoregressive Moving Average (ARMA) models, while a Fourier series is used to account for the variation of the mean and variance. Due to the use of random phase angles in the Fourier series, an ensemble of mean and variance variations is obtained. The methods of nonparametric statistics are used to determine the success of the modeling of nonstationarity. Justification of the method is obtained through comparison of rainflow cycle distributions and resulting fatigue lives of original and simulated loadings. Due to the relatively small number of Fourier coefficients needed together with the use of ARMA models, a concise description of complex loadings is achieved. The overall frequency content and sequential information of the load history is statistically preserved. An ensemble of load histories can be constructed on-line with minimal computer storage capacity as used in testing equipment. The method can be used in a diversity of fields where a concise representation of random loadings is desired. / Ph. D.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This dissertation aims to build a set of tools based on mathematical models to assist a rural electrification cooperative in taking strategic decisions on investing in electrical generation in face of erratic and non-periodic future scenarios. Time series analysis using the Box-Jenkins methods for forecasting was employed to construct the models to predict future energy consumption. Qualitative analysis of future scenarios using Kohler method, that is suited to regional applications, was used. An heuristic approach with hierarchical levels was employed to define the parameters of a mathematical model for the application of integer linear programming at a lower level. This mathematical program was used to optimize the location of photovoltaic solar power plants within a transformer substation area and its branches to minimize disbursements in assets investments, and operations and maintenance costs. The model was tested in a cooperative with six substations, 572 branches, 7,574 cooperative members and a 2,737 km length network. In results obtained was SARIMA models (1,1,1) x (0,1,1) 12. In total, obtained an increase of 1.292 kW for the six substations in the next five years, representing a disbursement R$ 17,170,000.00 if the cooperative to chooses to build a photovoltaic solar power plant to meet this increase of consumption. / A presente dissertação tem por objetivo o desenvolvimento de um modelo de previsão pautando-se em um conjunto de ferramentas com base em modelos matemáticos que auxilie uma cooperativa de eletrificação rural na tomada de decisões estratégicas de investimentos em geração frente a cenários aperiódicos futuros. Como metodologia foi utilizada a análise de séries temporais com métodos de Box-Jenkins para a construção de modelos que foram utilizados na previsão de consumo energético. Análise qualitativa de cenários futuros utilizando a metodologia de Kohler adequada a aplicações regionalizadas. Utilizou-se uma abordagem heurística e em níveis hierárquicos para definição dos parâmetros de um modelo matemático, para aplicação de programação linear inteira. A programação matemática foi usada num nível hierárquico inferior para otimizar a localização de usinas geradoras de energia elétrica por painéis fotovoltaicos em áreas de subestações e ramais visando minimizar desembolsos em geração, manutenção distribuição e operação. O modelo foi testado numa cooperativa com seis subestações, 572 ramais, cerca de 7.574 cooperados e com uma extensão em redes de 2.737 km. Como resultados foram obtidos modelos SARIMA (1,1,1) x (0,1,1) 12. No total foram previstos um aumento de 1.292 kW para as seis subestações nos próximos cinco anos, o que representa um desembolso R$ 17.170.000,00 caso a cooperativa opte na construção de uma usina solar fotovoltaica para suprir este aumento de consumo.