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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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Quantitative Methods of Risk Control
Marcinek, Daniel ; Hurt, Jan (advisor) ; Hendrych, Radek (referee)
This thesis deals with stock modelling using ARCH and GARCH time series. Important aspect of stock modelling is to capture volatility correctly. Volatility in finance is usually defined as a standard deviation of asset returns. Many different models, which are summarized in the first part of this thesis, are used to model volatility. This thesis focus on multivariate volatility models including multivariate GARCH models. An approach to constructing a conditional maximum likelihood estimate to these methods is given. Discussed theory is applied on real financial data. In numeric application there is a construction of a volatility estimates for two specific stocks using models described in the first part of this thesis. Using the same financial data various bivariate models are compared. Based on comparison using maximum likelihood a specific model for these stocks is recommended. Powered by TCPDF (www.tcpdf.org)
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Determinants forming attitudes of selected political parties from EU27 countries to the Turkish enlargement of the EU
Hendrych, Radek ; Šlosarčík, Ivo (advisor) ; Kostelka, Filip (referee)
The present thesis analyzes possible determinants shaping attitudes of selected relevant political parties from the EU27 Member States to the potential Turkish accession to the European Union. Bilateral relationships between the EU and the Turkish Republic have been evolving multifariously and long-windedly. However, the question of the direct Turkish participation in the EU's project remains unresolved, and still resonates across all stakeholders. The phenomenon of the eventual Turkish joining is a very topical issue. In particular, the views of the political parties on this particular problem are studied, since these subjects operate with an exclusive position in representative democracies. They symbolize the necessary interconnection between the state and society. Moreover, in the context of the eventual EU enlargement to Turkey, they will likely discuss its confirmation in parliamentary procedures, or they will mobilize voters and form their attitudes in the case of ratification referenda. The present thesis distinguishes between two main groups of explanatory variables. In regarding to the accepted theoretical framework, these are supposed to explicate the views of the selected political parties on the eventual Turkish enlargement qualifiedly. Particularly, the ideological and (general)...
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Estimation of parameters of clipped time series
Flimmel, Samuel ; Hudecová, Šárka (advisor) ; Hendrych, Radek (referee)
In some situations we cannot observe the original time series and instead, we record only binary data which express whether the values of the original series exceeded a certain threshold or not. The thesis deals with estimation of characteristics of the original series constructed from the binary (so called clipped or hard-limited) data, in particular in Gaussian ARMA models. We summarize some basic characteristics of the clipped series and describe their relation to the original ones. Some practical examples are provided as well. The estimation of parameters in AR(p) model is shown for the case of zero threshold. Using a similar approach, an estimator of the MA(1) model parameter is proposed and its properties are studied with emphasis on asymptotic variance. Subsequently, we propose an estimation procedure for AR(p) and MA(1) models with unknown (non-zero) threshold. The behaviour of our estimators is investigated in a simulation study, which provides a comparison with estimators constructed from the original data. Finally, a real data analysis is presented for an illustration. Powered by TCPDF (www.tcpdf.org)
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Econometric systems of simultaneous equations in life insurance
Hendrych, Radek
Title: Econometric systems of simultaneous equations in life insurance Author: Radek Hendrych Department: Department of Probability and Mathematical Statistics Supervisor: prof. RNDr. Tomáš Cipra, DrSc. Supervisor's e-mail address: cipra@karlin.mff.cuni.cz Abstract: In present work we deal with theoretical and practical issues related to econometric systems of (linear) simultaneous equations. In the first chapter we introduce to theoretical aspects of this problem. We devote considerable space to estimation procedures and comparisons of their properties, mention questions of identification, an inconsistency of OLS-estimates for the simultaneous modeling, tests of hypotheses specific to this area, dynamic systems and constructions of forecasts in models. In the second chapter we introduce selected basic concepts relevant to life insurance. In the third chapter we show the practical application of theoretical knowledge in the event of an econometric model of financial flows in the life insurance company operating on the Czech market. We compare ordinary estimation procedures (2SLS and 3SLS approach), perform some tests, which serve us to verify selected information on the studied model. We show the possibility of using residual bootstrap, including examples of use in the construction of confidence intervals....
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Non-linear models for financial time series and software tools for their analysis
Fučík, Jan ; Zichová, Jitka (advisor) ; Hendrych, Radek (referee)
This thesis deals with some time series models applicable in finance. First, the basic concepts are introduced and the linear AR models are presented. Afterwards, the reader becomes familiar with the nonlinear ARCH volatility models including their properties and the model-building. The generalized GARCH models are briefly mentioned. Another part of the thesis shows the usage of these models to real data in two available software products - R and Mathematica. The programs are compared from the point of the obtained results and the usability for the analysis of financial time series via the explained models. The description of the procedures and the attached CD with the outputs of the programs allow the reader to apply the models on his or her own data.
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The Lasso and its application to time series
Holý, Vladimír ; Prášková, Zuzana (advisor) ; Hendrych, Radek (referee)
This thesis first describes the Lasso method and its adaptive improvement. Then the basic theoretical properties are shown and different algorithms are introduced. The main part of this thesis is application of the Lasso method to AR, MA and ARCH time series and to REGAR, REGMA and REGARCH models. An algorithm of the adaptive Lasso in a more general time series model, which includes all above mentioned models and series, is developed. The properties of methods and algorithms are shown on simulations and on a practical example. Powered by TCPDF (www.tcpdf.org)
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Numerical study on simultanious equations
Šaroch, Vojtěch ; Lachout, Petr (advisor) ; Hendrych, Radek (referee)
Title: Numerical study on simultanious equations Author: Vojtěch Šaroch Department: Department of Probability and Mathematical Statistics Supervisor: doc. RNDr. Petr Lachout, CSc. Abstract: In this thesis we deal with simultaneous equation model. In first chapter we introduce to theoretical aspect of this problem, especially estimation procedures and their properties. We mention issues of identification and an inconsistency of OLS-estimates for the simultaneous modeling. In second chapter we introduce theory of estimation, especially we will focus on interval estimation and precision. We mention empirical approach too. In the third chapter we perform a numerical study on simple macroeconomic model on generated dates. We are interested in properties interval estimations of parameters, the convergence rate, difference between empirical and theoretical extimation etc. Keywords: simultaneous equations model, interval estimation, empirical estimation 1
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Tests for time series linearity
Melicherčík, Martin ; Prášková, Zuzana (advisor) ; Hendrych, Radek (referee)
Title: Testing for linearity in time series Author: Martin Melicherčík Department: Department of Probability and Mathematical Statistics Supervisor: doc. RNDr. Zuzana Prášková, CSc., Department of Probability and Mathematical Statistics Abstract: In the first part of the thesis, a necessary theoretical base from time series analysis is explained, which is consequently used to formulate several tests for linearity. According to variety of approaches the theory includes wide range of knowledge from correlation and spectral analysis and introduces some basic nonlinear models. In the second part, linearity tests are described, classified and compared both theoretically and practically on simulated data from several linear and nonlinear models. At the end, some scripts and hints in R language are introduced that could be used when applying tests to real data. Keywords: linear time series, bispectrum, testing for linearity, nonlinear models
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Principal components analysis and its applications
Dubová, Mária ; Hendrych, Radek (advisor) ; Prášková, Zuzana (referee)
In the present thesis, we deal with the principal components analy- sis. In the first of this text, we study different aspects of principals components, for instance, their derivation for a multidimensional random vector from general distribution or their calculation based on a covariance or correlation matrix. It is also important to choose the proper number of principal components for reducing the dimensionality of data in order to preserve most of information. Theoretical knowledge are illustrated with several examples. In the second part of the thesis, we focus on the value at risk. This term is defined in the text also with seve- ral usual formulas to calculate it. Then, we deal with a practical application of this concept and the principal component analysis. Concretely, we analyse the portfolio of some different interest rates to obtain the value at risk in some cases. 1
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