
Descriptive statistics in R with application on real data
Pirohová, Eva ; Bašta, Milan (advisor) ; Šulc, Zdeněk (referee)
The aim of this thesis is to introduce the statistical software R, its use in descriptive statistics and to explain the principle of entering commands and functions in R. In the theoretical part of the thesis the user will be given the basic information about descriptive statistics and the key principles of R software. An important part of the thesis is an illustration of functions and codes which are to be entered into a script or a command window. The practical part represents the way of applying descriptive statistics on real data by using functions and codes in R, including the corresponding types of graphs. There is always an explanation following the example. This thesis contains all the important information which those who start with basic statistical analysis and R software should know. Despite the fact that working with R may be rather complicated at the beginning, this thesis is written in such a way so that it can be read by a beginner in R and statistical analysis.


Population viability analysis of endangered species in Czech Republic
Šťastná, Andrea ; Helman, Karel (advisor) ; Bašta, Milan (referee)
Diploma thesis analyzes the viability of the selected species populations in the Czech Republic. The thesis is divided into two main parts. The first part contains a stochastic model simulating possible scenarios of the Eurasian lynx population size in the Czech Republic. For this model program Vortex was used. The second part is focused on Time series analysis of the Grey Partridge and the Common Kingfisher population, where data was obtained from the Czech Society for Ornithology. This analysis aims on identification of factors that may affect the viability of the two bird species.


Analysis of debt development in the Czech Republic
Krýslová, Petra ; Bašta, Milan (advisor) ; Helman, Karel (referee)
The aim of this diploma thesis is to analyze the development of the total volume of debt in the Czech Republic and the analysis separately for the household sector and nonfinancial corporations. From economic theoretical assumptions it can be concluded that there is a correlation between the amount of loans and GDP development or between credit and economic cycle. The thesis is divided into three parts. The first part made up of chapters 1 to 4, describes the theory used further in the text. The second part, Chapter 5, describes the specific time series used in the thesis, i.e. The time series of the volume of debt for the Czech Republic, GDP and interest rates. Interest rates and the volume of debt are further broken down by maturity and also by two selected sectors. The last part, Chapter 6, focusing on cointegration analysis, ADL and error correction models, attempts to capture shortterm and longterm relationships between the time series.


Volatility models in R
Vágner, Hubert ; Bašta, Milan (advisor) ; Flimmel, Samuel (referee)
This diploma thesis focuses on modeling volatility in financial time series. The main approach to modelling volatility is using GARCH models which can capture the variability of conditional volatility of time series. For modelling a conditional mean value in time series are used ARMA models. In the series there are usually not fulfilled the assumption of earnings normality, therefore, are the earnings in most cased characterized by the leptokurtic shape of distribution. The thesis introduces some more distribution types, which can be more easily used for the earnings distribution  above all the Students t distribution. The aim of the thesis in the first part is to present the topic of financial time series and description of the GARCH models including their further modification. There are used e.g. IGARCH or other models capturing asymmetric impact of shocks such as GJRGARCH. The second part deals with generated data, where are more in detail explored the volatility models and their behavior in corresponding financial time series. The third part focuses on the volatility estimation and forecasting for the financial time series. Firstly this concerns development of stock index MICEX secondly currency pair Russian Ruble to Czech Crown and eventually price development of the Brent crude oil. The goal of the third part is to present the impacts on volatility of chosen time series applied on the example of economic sanctions against Russia after annexation of the Crimea peninsula which happened in the first quarter 2014.


Regression analysis and splines
Benko, Milan ; Bašta, Milan (advisor) ; Komárek, Arnošt (referee)
The aim of this Bachelor's thesis is to introduce the basic concepts of regression analysis and subsequently regression splines as parametric models for regression function. I have looked upon the main characteristics of regression splines (coherence, coherence of derivations, the choice of placement and a number of knots). Further on in the thesis I have studied two bases as the examples of regression splines (truncated power basis and Bspline basis). I have also presented a model of natural cubic splines and a suitable basis for its representation has been derived. In the other part of my thesis I have looked upon the use of natural splines in order to increases the appraisal precision of regression function, mean square error formula has been derived and I have been trying to find out and illustrate under what conditions the use of natural splines is applicable. The thesis is complemented with a Monte Carlo Simulation, contextualized into models of splines. The results show that the criteria commonly used for the choice of a model ($\R_{adj}^2$, $PRESS$ statistic, hypothesis testing) do not always enable us to choose the right model in order to achieve the greatest precision of the estimation of regression function. All the calculations are done in R software and are in the electronic attachment....

 

Local polynomial regression
Cigán, Martin ; Bašta, Milan (advisor) ; Maciak, Matúš (referee)
This thesis examines local polynomial regression. Local polynomial regression is one of nonparametric approach of data fitting. This particular method is based on repetition of fitting data using weighted least squares estimate of the parameters of the polynomial model. The aim of this thesis is therefore revision of some properties of the weighted least squares estimate used in linear regression model and introduction of the nonrobust method of local polynomial regression. Some statistical properties of the local polynomial regression estimate are derived. Conditional bias and conditional variance of the local polynomial regression estimate are then approximated using Monte Carlo method and compared with theoretical results. Powered by TCPDF (www.tcpdf.org)


Normality and its testing
Hájek, Štěpán ; Bašta, Milan (advisor) ; Klebanov, Lev (referee)
This thesis is concerned with normality and its testing. We often encounter with this topic when using statistical tests and models. Among others, examples such as t tests, analysis of variance and linear regression might be given. In this thesis these tests and models are overviewed and the consequences of the violation of the normality assumption are briefly mentioned. The following section describes statistical tests of normality. For example ShapiroWilk test or AndersonDarling test are explored. For each test of normality is given test statistic and conditions for rejection of the null hypothesis. The last section provides a simulation study. The first part of this study is devoted to exploring whether the empirical relative frequency of Type I error corresponds to the nominal significance level of the test. The second part of the simulation study explores the power of normality tests against various alternatives. The results are summarized and discussed. 1


Technical analysis based on trade volumes and their effectivity from the point of view of future price movements
Chval, David ; Bašta, Milan (advisor) ; Zichová, Jitka (referee)
This Bachelor Thesis studies methods of technical analysis based on trade volume. The first two chapters are theoretical. They describe financial markets, their functions, properties and methods used in analysis of financial instrument. In the next section is described efficient market hypothesis, forms of efficiency and tests of this hypothesis. The third chapter is analytical. The idea that extreme trading activity predict future increase, or decrease of stock prices is investigated. Here is described methodology, data aquisition, analysis results and comparison with other similar research.


Modelling and forecasting seasonal time series
Jantoš, Milan ; Bašta, Milan (advisor) ; Helman, Karel (referee)
In this Master Thesis there are summarized basic methods for modelling time series, such as linear regression with seasonal dummy variables, exponential smoothing and SARIMA processes. The thesis is aimed on modelling and forecasting seasonal time series using these methods. Goals of the Thesis are to introduce and compare these methods using a set of 2184 seasonal time series followed by evaluation their prediction abilities. The main benefit of this Master Thesis is understanding of different aspects of forecasting time series and empirical verification of advantages and disadvantages these methods in field of creating predictions.
