Title: Selected problems of financial time series modelling Author: Radek Hendrych Department: Department of Probability and Mathematical Statistics (DPMS) Supervisor: Prof. RNDr. Tomáš Cipra, DrSc., DPMS Abstract: The present dissertation thesis deals with selected problems of financial time series analysis. In particular, it focuses on two fundamental aspects of condi- tional heteroscedasticity modelling. The first part of the thesis introduces and discusses self-weighted recursive estimation algorithms for several classic univariate conditional heteroscedasticity models, namely for the ARCH, GARCH, RiskMetrics EWMA, and GJR-GARCH processes. Their numerical capabilities are demonstrated by Monte Carlo experiments and real data examples. The second part of the thesis proposes a novel approach to conditional covariance (correlation) modelling. The suggested modelling technique has been inspired by the essential idea of the multivariate orthogonal GARCH method. It is based on a suitable type of linear time-varying orthogonal transformation, which enables to employ the constant conditional correlation scheme. The correspond- ing model is implemented by using a nonlinear discrete-time state space representation. The proposed approach is compared with other commonly applied models. It demon- strates its...

Diploma thesis extends my Bachelor´s thesis, which was about methods of time distribution of precipitations and differences in that distribution within a small area. The first part of the paper describes the formation and distribution of precipitation, typical variation of precipitation and some characteristics, revealing and describing the behaviour of rainfall in a given station. Following part describes possible methods of evaluation of time distribution. Statistical methods are presented mainly here. Here described methods and evaluations are subsequently applied in time series of daily precipitations, which has been available for this work for the Jenin creek basin. The analysis is focused on characteristics and evaluation of rainfall between terms 1980 - 1988 and 2005 - 2013. The results show us some differences between terms in rainfall characteristics. However, mostly they are not statistically significant. The work also evaluates differences in rainfall totals between rainfall stations Jenín and Dolní Dvořiště (approximate distance of the stations is 4 km) in 2005 - 2013 term. During the evaluation it comes to differences in rainfall totals. They are highly variable and they don´t have neither constant direction nor size.

This diploma thesis deals with inventory optimalization in Poex Velke Mezirici JSC which operates on food markets. The main goal is to evaluate current company's situation based on collected data and with help of mathematical models propose steps leading to higher eficiency of company's supply chain. Another goal is to create model which will help to predict future demand based on the data of it's past development.

Submitted dissertation is focused on methods of robust normality testing and applications of robust tests in verifying hypothesis of the weak form of efficiency in stock markets. In the dissertation, theory of efficient markets and approaches to verifying the weak form of market efficiency and normality assumption are being discussed. Novel robust testing procedures of testing normality are proposed in this work to overcome shortcomings of classical normality tests in the field of financial data, which are typical with occurrence of remote data points and additional types of deviations from normality. Results of power simulation study of classical and robust tests of normality against several types of alternative distributions, i.e. symmetric heavy-tailed, symmetric light-tailed, asymmetric heavy-tailed, asymmetric light-tailed, selected mixtures of normal distributions and outlier models, are presented. Based on outcome of the power simulation study, selected normality tests were consequently used to verify the weak form of efficiency in stock markets in the Czech Republic, Hungary, Austria, Germany, Slovakia, United States and Japan during years 2000-2009. In addition to selected classical and robust normality tests, Ljung-Box portmanteau test was also used. In conclusion, there is a discussion and comparison of results carried out and future trends of these markets are outlined.

The thesis deals with the demographic analysis of Kutná Hora region, with a focus on social services in the years 2005-2014. Between the monitored demographic indicators include the status and structure of the population, birth rate, mortality rate, rates of marriage, the divorce rate, migration and related indicators. The indicators were selected on the basis of their impact on social services. The values of the selected indicators of the region are also compared with the values of the whole of the Czech Republic. Most of the indicators of the region has the same trend as the average of the values of the Czech Republic, but there are even specific differences that characterize the region under consideration. All the data needed to draw up an analysis has been collected from the Czech Statistical Office. To assess the development of the various demographic indicators have been used by the elementary characteristics of the time series and the trend function. The prediction was made after the selected demographic indicators of the region of Kutná Hora in the year 2015 and 2016, which have a particular impact on social services. Furthermore, an analysis was made of the current state of social services in the region, where he was examined, the number of providers of social services, including their capacity. On the basis of the results of the analyses are in the conclusion drawn up proposals and recommendations for possible improvement of the situation in the framework of the social services in the region of Kutná Hora.

The environment is an important part of human life, which greatly affects the quality of human health and the entire population. On the quality of the environment is given ever greater emphasis, since there is an increase in the negative anthropogenic effects. To avoid these impacts or reduce their consequences should protect the environment. The important part is sustainable development in order to keep a full-fledged environment to future generations. In this thesis I analyze the main pollution by pollutants in the years 2000-2013 from all stationary sources in the district of Karvina, and from mobile sources of the Moravian-Silesian Region. Based on the statistical data of the Czech Hydrometeorological Institute, I processed an analysis of time series methods, has chosen trendy model with a forecast of future progression. For the years 2014 - 2016, I calculated the prediction of emitted pollutants.

This diploma thesis analysis selected indicators from beekeeping in 2005-2015 in region Vysočina. Diploma thesis analysis, development of number of beehives, number of beekeepers, number of beehives per beekeeper and production of honey in region Vysočina. Diploma thesis calculate trends of development of these time series and predict their development to the future. These indicators are very interesting, not just because of production of honey and recreational function of beekeeping, but mainly because of pollination. Without bees crop yields would decrease rapidly and from landscape would disappear a lots of plants. That is why it is important to whole agriculture if they can count on pollination by bees. Diploma thesis also analysis numbers of beehives and numbers of beekeepers divided to groups by number of beehives per beekeeper in region Vysočina and their development between years 2010 and 2015. Thesis also contains questionnaire made in population of region Vysočina. This questionnaire finds out consumption of honey of population of Vysočina and their habits and preferences in shopping and consuming honey. Conclusion of thesis is prediction of development of beekeeping in Vysočina and recommendation of future steps for further development of this field.

The subject of this thesis is the analysis of household expenditures changes (families with two parents and one-parent families) in the Czech Republic based on CZ-COICOP. The theoretical part includes types of Czech households, (in)completeness of families, existing findings on the management of Czech households with children and the way how Czech Statistical Office uses to collect and analyze data, terms like income or expenditure of households and classification of individual consumption by purpose. The practical part consists of evolution of revenue and expenditure of full and not full families witch children in the years 2004-2015, based on CZ-COICOP. Income and expenditures are evaluated not only in real terms, but even more thanks index which shows proportions of every section of expenditure to total household consumption. Last charter is about index of price ganges in European Union during year 2015.

Prediction of energy load profiles is an important topic in Smart Grid technologies. Accurate forecasts can lead to reduced costs and decreased dependency on commercial power suppliers by adapting to prices on energy market, efficient utilisation of solar and wind energy and sophisticated load scheduling. This thesis compares various statistical and machine learning models and their ability to forecast load profile for an entire day divided into 48 half-hour intervals. Additionally, we examine various preprocessing methods and their influence on the accuracy of the models. We also compare a variety of imputation methods that are designed to reconstruct missing observation commonly present in energy consumption data.

The aim of this thesis is to evaluate the usage of synonyms in teaching Russian language at high schools. The theoretical part of this thesis outlines the issues of synonyms and synonymous series from the linguistic (paradigmatic relations, semantics, stylistic) and linguodidactic point of view. The theoretical part also includes the issue of vocabulary from the didactic point of view. Furthermore, in the practical part, the diversity of synonyms used in curriculum of Russian language teaching are evaluated as well as the methods of demonstration and practising of such curriculum. In the final part of this thesis my own concepts for working with synonyms in teaching Russian language at high schools are suggested. KEYWORDS: synonyms, synonymous series, foreign languages, vocabulary, Russian language teaching