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Seasonal state space modeling
Suk, Luboš ; Cipra, Tomáš (advisor) ; Zichová, Jitka (referee)
State space modeling represents a statistical framework for exponential smoo- thing methods and it is often used in time series modeling. This thesis descri- bes seasonal innovations state space models and focuses on recently suggested TBATS model. This model includes Box-Cox transformation, ARMA model for residuals and trigonometric representation of seasonality and it was designed to handle a broad spectrum of time series with complex types of seasonality inclu- ding multiple seasonality, high frequency of data, non-integer periods of seasonal components, and dual-calendar effects. The estimation of the parameters based on maximum likelihood and trigonometric representation of seasonality greatly reduce computational burden in this model. The universatility of TBATS model is demonstrated by four real data time series.
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Multivariate ANOVA as a tool for the analysis of financial and economical data
Hájková, Anna ; Zichová, Jitka (advisor) ; Anděl, Jiří (referee)
This diploma thesis is dedicated to the analysis of variance with an application to real data, which is used to the comparison of means of several random samples. The aim of this thesis is to inform about multidimensional ANOVA. The teoretical part contains a description of two approaches, namely LR test and UI test. These tests are described in detail and then applied to three hypothesis. For the better understanding, the methods, studied in the theoretical part, are applied to a dataset of clients of an insurance company. The program Mathematica 9.0 was chosen as an appropriate software tool for the analysis of data.
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Time series models with exogenous variables and their application to economical data
Vaverová, Jana ; Zichová, Jitka (advisor) ; Cipra, Tomáš (referee)
This thesis deals with analyzing multivariate financial and economical data. The first section describes the theory of multivariate time series and multivariate ARMA models. The second part deals with some models with exogenous variables such as simultaneous equations models and ARMAX model. In the final chapter, the described theory is applied to analyze the reciprocal dependence of time series of inflation rates and dependence of inflation rates on various macroeconomical indicators. The results were obtained by software Mathematica 8, Mathematica 10, EViews and R. Powered by TCPDF (www.tcpdf.org)
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Econometric Analysis of Financial Data
Baniar, Matúš ; Zichová, Jitka (advisor) ; Cipra, Tomáš (referee)
Econometric Analysis of Financial Data Author: Matúš Baniar Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Jitka Zichová, Dr. Abstract: In some occasions, financial data can be represented as a combination of cross-sectional and time-series information. Hence it could be convenient to consider a system of econometric equations for modeling such data sets. At the beginning of this thesis, we describe general definitions and we talk about different types of variables from the perspective of exogeneity. Later, we describe some specific cases of these equations: SUR system, simultaneous equation models and the model of vector autoregression. For selected models, we also discuss estimation methods and their properties. In the final section, the described approach is applied to real financial data making use of appropriate software. Keywords: exogeneity, SUR system, simultaneous equations, VAR
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Econometric Analysis of Financial Data
Baniar, Matúš ; Zichová, Jitka (advisor) ; Cipra, Tomáš (referee)
Econometric Analysis of Financial Data Author: Matúš Baniar Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Jitka Zichová, Dr. Abstract: In some occasions, financial data can be represented as a combination of cross-sectional and time-series information. Hence it could be convenient to consider a system of econometric equations for modeling such data sets. At the beginning of this thesis, we describe general definitions and we talk about different types of variables from the perspective of exogeneity. Later, we describe some specific cases of these equations: SUR system, simultaneous equation models and the model of vector autoregression. For selected models, we also discuss estimation methods and their properties. In the final section, the described approach is applied to real financial data making use of appropriate software. Keywords: exogeneity, SUR system, simultaneous equations, VAR
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Estimations of risk with respect to monthly horizon based on the two-year time series
Myšičková, Ivana ; Houfková, Lucia (advisor) ; Zichová, Jitka (referee)
The thesis describes commonly used measures of risk, such as volatility, Value at Risk (VaR) and Expected Shortfall (ES), and is tasked with creating models for measuring market risk. It is concerned with the risk over daily and over monthly horizons and shows the shortcomings of a square-root-of-time approach for converting VaR and ES between horizons. Parametric models, geometric Brownian motion (GBM) and GARCH process, and non-parametric models, historical simulation (HS) and some its possible improvements, are presented. The application of these mentioned models is demonstrated using real data. The accuracy of VaR models is proved through backtesting and the results are discussed. Part of this thesis is also a simulation study, which reveals the precision of VaR and ES estimates.
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Autocorrelation and decomposition methods in economic time series analysis
Filka, Jakub ; Zichová, Jitka (advisor) ; Cipra, Tomáš (referee)
The goal of this bachelor thesis is to give a basic theoretical background for working with time series with the usage of autocorrelation and decomposition methods, as well as to apply these methods on real data in selected software. The interpretation of the results is closely related to the comparison of advantages and disadvantages of the methods. We have used the software Wolfram Mathematica and NCSS. The main contribution of the thesis is the connection of both theoretical and practical approach, which was not performed similarly in Czech or Slovak literature in the time of elaborating the thesis. Keywords: time series, autocorrelation methods, decomposive methods, Wolfram Mathematica Powered by TCPDF (www.tcpdf.org)
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Means testing with an application to economic data
Došel, Jan ; Zichová, Jitka (advisor) ; Hlávka, Zdeněk (referee)
Title: Means testing with an application to economic data Author: Jan Došel Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Jitka Zichová, Dr., Department of Probability and Mathema- tical Statistics Abstract: The bachelor thesis deals with multivariate analysis of variance as a sta- tistical tool for comparing means of several random samples. In theoretical part, basic terms are described. Furthermore, a test statistic is derived from likelihood functions. The method is demonstrated by a simulation study in practical part. Keywords: analysis of variance, hypothesis testing, multivariate normal distribu- tion, likelihood function 1
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Dependence analysis of categorical data from banking
Khýr, Miroslav ; Zichová, Jitka (advisor) ; Mazurová, Lucie (referee)
Title: Dependence analysis of categorical data from banking Author: Miroslav Khýr Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Jitka Zichová, Dr., Department of Probability and Mathema- tical Statistics Abstract: The aim of this work is describing in detail the theory of the log - linear expansion and graphical models for random vectors with a discrete distribution. Such vector can be used for modeling categorical variables for example in a po- pulation of borrowers by a bank . We show how to estimate the probability of an individual category. We use a log - likelihood function. Independence graph can represent conditional independence of discretely distributed random variables. Using this theory, especially using deviance as test statistics, we can examine whether same data correspond to the selected graphical model. At the end of this work we apply the described theory to real data and determine the graphical mo- del best fitting the dependence structure in a database from banking. From this graph we can deduce which variables are dependent and which are independent. Keywords: Log - linear expansion, graphical model, log - likelihood function ,de- viance.
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Financial time series modelling with trend
Studnička, Václav ; Zichová, Jitka (advisor) ; Prášková, Zuzana (referee)
Various models can be used for the analysis of financial time series. This thesis focuses mainly on two models; non-linear trend model and linear trend model. First chapter is theoretial, there is an introduction to the theory of time series and to the autoregressive process. Second chapter is also theoretical and it focuses on a description of both non-linear and linear trend model including derivations of im- portant properties of these models; moreover, it contains theory for the modelling of financial time series and predictions. Last chapter contains simulations of two mentioned models and estimations of their parameters, Wolfram Mathematica is used for all simulations. 1
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