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The Analysis of Selected Monthly Temperature Time Series in Europe
Janoutová, Eva ; Helman, Karel (advisor) ; Bašta, Milan (referee)
This Bachelor´s thesis is focused on analysis of time series of monthly mean temperatures and monthly maximum temperatures. These temperatures are observed on eight meteorological stations between the years 1949-2013. The data were obtained from the database of European Climate Assessment & Data. Stations are divided into two groups according to Köppen climate classification. The purpose of this bachelor thesis is to observe and compare the development of individual time series in both groups using basic characteristics and methods based on time series decomposition and to verify that the observed station´s climate type classification is correct. Another aim is to verify the hypothesis that monthly mean temperatures and monthly maximum temperatures has increased in the observed period.
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GARCH models and R
Jánoš, Andrej ; Bašta, Milan (advisor) ; Hejdová, Martina (referee)
The work is devoted to the concept of volatility and the basic models of volatility ARCH and GARCH. Firstly, volatility, properties of volatility, general structure of the models and historical volatility is described. Then the ARCH and GARCH volatility models are introduced and their properties, estimation methods and the possibility of implementation of these models in modeling and forecasting volatility are discussed. A substantial part of this work is a detailed application of the described models to some particular time series (both simulated and real) using the R program. We analyze the real data capturing the evolution of Prague stock index PX. The key aspect of the work is to provide enough theoretical knowledge and practical skills for a reader to fully understand the mentioned models and to be able to apply them in practise.
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Mixed Models and Their Application in Medical Data Analysis
Mohammad, Adam ; Malá, Ivana (advisor) ; Bašta, Milan (referee)
This bachelor thesis deals with the description of the linear mixed model. At first, the model is described theoretically and the basic terms, model specification, estimation of unknown parameters, model-building and model diagnostics are explained. In addition, types of data for which the model may be applied are listed and some examples of applications in medicine are given as well. The second part of this thesis deals with the practical application of the model for analysis of longitudinal data from a medical research. The data contain information about 12 patients to whom a drug named theophylline was given and the concentration of this drug in blood was measured within one day. By statistical software R the dependency of the concentration on time, dose and weight of the patient is described. However the results of the analysis show that the dependency of concentration on time cannot be described by a simple function, therefore this dependency has to be described and the data modified prior to application of linear mixed model on data. The other possibility is to use a different model.
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Analysis of time series of passengers volume in selected European airports
Mayerlová, Evelyn ; Helman, Karel (advisor) ; Bašta, Milan (referee)
This bachelor thesis is focused on analysis of monthly time series of passengers volume in three selected European airports (Airport Vaclav Havel -- Prague-Ruzyně, Airport Franz Josef Strauß -- Munich and Airport Schwechat -- Vienna). This thesis examines monthly volume data of passengers in 2001-2013 period. The data were collected from the Eurostat web pages, airport databases and by direct communication between the author and the individual airports. The major goal of this thesis is to explore the development of the time series. In the analysis we use basic characteristics of time series and selected basic methods for modelling the trend and seasonal components. The ambition of this thesis is to figure out, if the numbers of transported persons differ in different months of the year,if and how has a popularity of air transport increased and to compare time series of different aiports.
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The average wage and GDP - relationships and links
Bieliková, Nikol ; Arltová, Markéta (advisor) ; Bašta, Milan (referee)
The thesis describes interactions and relationships between selected economic indicators. These indicators are the gross domestic product and the average gross monthly wage. The analysis of these selected indicators, are made for the Czech Republic and Slovakia. The work has four main parts, which are divided into several other sections. The first defines the concept of national accounting, the second part contents gross domestic product, the method of its calculating and the frequency of compilation. In the third section is described the field theory of wages and salaries and the concepts such as minimum wage, the average gross monthly wage and median wage and salary are defined. In this two chapters are compared selected countries on the basis of the tables and graphs of selected indicators. The last chapter analyzes the relationships between selected economic indicators in selected countries based on quarterly data from the years 2001-2013.
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Analysis of temperature time series for selected places in the United States in the years 1964–2013
Libotovský, Patrik ; Helman, Karel (advisor) ; Bašta, Milan (referee)
This bachelor thesis is focused on analysis of time series of monthly average temperatures measured at seven selected meteorological stations located in the territory of the United States in the period 1964-2013. The data were taken from publicly available database US National Climatic Data Centrer. The aim of this work is to determine the evolution of selected time series. Analyzed data are used to obtain findings about the similarities and differences between them. For this analysis, we use basic characteristics and methods based on decomposition of time series to describe the trend and seasonal ingredients. Another aim is to test the hypothesis whether in the monitored period increased the avarage monthly temperature on the territory United States. The thesis is divided into two parts. The first part provides a theoretical description of the selected methods for time series analysis. The second part is devoted to the analysis itself.
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Quantile Regression
Procházka, Jiří ; Bašta, Milan (advisor) ; Malá, Ivana (referee)
The thesis deals with brief introduction of the quantile regression theory. The thesis is divided into three thematic parts. In the first part the thesis deals with general introduction to the quantile regression, with theoretical aspects regarding quantile regression and with basic approaches to estimation of quantile regression parameters. The second part of the thesis focuses on general and asymptotic properties of the quantile regression. Goal of this part is to compare the quantile regression with traditional OLS regression and outline its possible application. In the third part the thesis describes statistical inference, construction of the confidence intervals and testing statistical hypotheses about quantile regression parameters. The goal of this part is to introduce traditional approach and the approach based on resampling procedures and in the end of the day perform mutual comparison of different approaches eventually propose partial modification.
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Classification and Regression Trees in R
Nemčíková, Lucia ; Bašta, Milan (advisor) ; Vilikus, Ondřej (referee)
Tree-based methods are a nice add-on to traditional statistical methods when solving classification and regression problems. The aim of this master thesis is not to judge which approach is better but rather bring the overview of these methods and apply them on the real data using R. Focus is made especially on the basic methodology of tree-based models and the application in specific software in order to provide wide range of tool for reader to be able to use these methods. One part of the thesis touches the advanced tree-based methods to provide full picture of possibilities.
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Functional data analysis and modeling age-specific mortality and age-specific fertility
Bezchlebová, Daniela ; Bašta, Milan (advisor) ; Dotlačilová, Petra (referee)
The aim of this thesis is to analyze two major indicators representing the processes of natural changes in population, which are not influenced by age structure -- age specific fertility rate and age specific mortality rate and to introduce functional data analysis, which has recently become increasingly applied in many scientific fields. The functional data analysis is introduced on the Czech demographic data set for more than last sixty years. The thesis briefly describes historical development of mortality and fertility and also describes selected methods of functional data analysis by using statistical program R. Functional data analysis provides a wide variety of graphics tools to explore the data which we called functional and help us to explore all typical and atypical features, identify outliers etc.
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Using of transformations in regression analysis
Housková, Markéta ; Bašta, Milan (advisor) ; Helman, Karel (referee)
This Thesis deals with the using of transformations in model of regression analysis. The first part of the Thesis summarizes the theoretical findings of the regression models, assumption of these models and the possibility of using different types of transformations in the event non-compliance of regression models. The practical part of this Thesis deals with regression analysis of real dataset on school readiness of children from the district of Kolín in 2013 and using transformations in the selected regression model.
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