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Linear and bilinear models for time series from economics and finance
Kotrbová, Anežka ; Zichová, Jitka (advisor) ; Prášková, Zuzana (referee)
This bachelor thesis deals with linear and bilinear models used for modelling time series data applicable in economy and finance. The thesis consists of a theoretical and a practical part. The theoretical part briefly describes ARMA and bilinear process, issues of linear model identification, estimation of the parameters and moment properties of ARMA(1, 1) a BL(1, 0, 1, 1). The typical characteristics of bilinear models and the quality of the estimated parameters are examined by the simulation study in software Mathematica 10. The acquired findings are applied in search for a suitable model for time series of share prices of the company ČEZ. Powered by TCPDF (www.tcpdf.org)
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Unit root testing with applications to financial time series
Pechmanová, Kateřina ; Zichová, Jitka (advisor) ; Hendrych, Radek (referee)
This work deals with linear ARMA processes, which are intended to describe the behavior of time series, and also with analysis of selected time series. First, the basic concepts are introduced together with the descriptions of the ARMA models. Further, the Dickey-Fuller test for a unit root, as an approach to the verification of nonstationary time series, is introduced. An important part is the practical application of these models and tests on simulated and real data. Real analyzed data capture developments in the exchange rate of Czech crown against Euro. All calculations were performed in the Mathematica software. Powered by TCPDF (www.tcpdf.org)
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Selected problems and methods in multivariate data analysis
Goduľová, Lenka ; Zichová, Jitka (advisor) ; Hurt, Jan (referee)
Title: Selected problems and methods in multivariate data analysis Author: Lenka Goduľová Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Jitka Zichová, Dr. Abstract: The bachelor thesis deals with processing multidimensional data. The task was to apply selected methods on financial data. The thesis is composed of the theoretical section and the analysis of a particular database. The first four chapters deal with basic relations and definitions concerning random vector and variable, multidimensional data and the independence test in a contingency table. The following section is devoted to defining the particular methods selected: cluster analysis and discriminant analysis. In the practical section these methods are applied to a database of clients of a German bank. Keywords: random vector, multivariate distribution, multivariate random variable, contingency table, cluster analysis, discriminant analysis.
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Pensions from the point of view of utility theory
Kudlík, Michal ; Cipra, Tomáš (advisor) ; Zichová, Jitka (referee)
This work deals with pensions from the perspective of utility theory. We list several basic principles, characteristics of pensions and their classification. Part of the work is also the utility theory from the ordinal point of view of utility theory as well as in terms of cardinal utility functions. Afterwards, we formulate the tasks for the selected utility functions, which we will try to optimize by using utility functions. We transfer the task of maximizing objective function to the task with extreme bound corresponding to various annuity markets which we will solve by theory of Lagrange multipliers. Final result of the work should be calculation of annuity equivalent wealth per common utility function Constant relative risk aversion (CRRA) using different relative risk aversions and showing the optimum consumption strategy for pensioners calculated based on mortality tables for Czech republic from 2012. 1
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Financial risks with copulas
Prelecová, Natália ; Hurt, Jan (advisor) ; Zichová, Jitka (referee)
The aim of this thesis is the thorough description of the copula theory. It deals with the theory's basic definitions, classes and characteristics. In addition, relations between copulas and dependence measures are explained. Furthermore, we evaluate the possibilities of copula's parametres estimation and selecting the right copula for real data. Then, the copula theory is interconnected with the basic risk measures in finance. We describe the elementary categorization of financial risks and standard risk measurement approaches. We also define basic risk measures with the emphasis on value at risk. Lastly, we present a real data case study of a selected portfolio.
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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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