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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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Smooth Transition Autoregressive Models
Khýr, Miroslav ; Zichová, Jitka (advisor)
The aim of this work is describing theory of smooth transition autoregressive models, namely LSTAR and ESTAR models. The essential part of the work is devoted to the derivation of tests for linearity against the alternative of the re- levant nonlinear model. There is also shown how to estimate the parameters of these models along with the selection procedure between the LSTAR and the ESTAR model. A simulation study was carried out, which deals with the power of linearity tests. At the end of the thesis, we applied the theory to some real data and we estimated the appropriate model for their representation. 1
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Linear volatility modeling in financial time series
Kollárová, Dominika ; Zichová, Jitka (advisor) ; Hendrych, Radek (referee)
The aim of this master thesis is to introduce models belonging to ARCH(∞) representation where a time series volatility is modelled as a linear function of squared residuals. Specifically, the thesis deals with models IGARCH, FIGARCH and HYGARCH that are used to analyse, model and predict a development of financial time series. Definition and graphical illustration of individual models together with their application on real data, is supplemented by a simulation study of first-order FIGARCH model.
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Nonlienar volatility modeling in financial time series
Sychova, Maryna ; Zichová, Jitka (advisor) ; Hlávka, Zdeněk (referee)
In this work we want to examine selected models with nonlinear volatility and their properties. At the beginning we define models with non-constant variance, especially ARCH, GARCH and EGARCH models. Then we study the probability distributions that are mainly used in the EGARCH model. Then we focus on the EGARCH model, describe the conditions for stationarity and invertibility of the model, define diagnostic tests and QMLE estimates of parameters. In the last chapter we perform simulation studies of the selected models and their application to real data. 1
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Index of dispersion for discrete distributions
Semjonov, Valerij ; Hudecová, Šárka (advisor) ; Zichová, Jitka (referee)
This thesis deals with the index of dispersion for discrete distributions. In the first chapter, we define the sample index of dispersion and describe it's basic properties , specifically for the Poisson distribution. An asymptotic distribution of the sample index of dispersion will be derived for the Poisson and some other distributions. In the second chapter, we describe the index of dispersion test and determine it's approximate power against some specific alternatives. The third chapter is dedicated to a simulation study in which statistical properties of the test are investigated. Empirical estimation of the power of the test will be compared with the analytical results obtained in the second chapter.
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Stochastic claims reserving with double chain ladder
Javůrková, Tereza ; Pešta, Michal (advisor) ; Zichová, Jitka (referee)
This thesis deals with an important problem of insurance which is forecasting outstanding claims liabilities. It describes the Chain-Ladder method, the basic method for forecasting outstanding claims, and then it's extention to Double Chain-Ladder method. It also uses the number of reported claims for a beter estimate. The final forecast is calculated from the IBNR and RBNS reserves which are estimated separetly. Finly we aplly those methods to a real life dataset. The results shows differences betwen those two methods and different ways of programming. 1
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Nonparametric Nonlinearity Testing in Time Series
Dudlák, Oliver ; Zichová, Jitka (advisor) ; Prášková, Zuzana (referee)
The aim of this bachelor thesis is nonparametric nonlinearity time series testing by using Q-tests and BDS-test. We describe theoretically each of the tests and then use them on simulated and real historical data. For tested time series we firstly try to identify linear model ARMA(p,q). Then we apply the tests on the estimated white noise to test the assumption of independence or noncorrelation and verify the accuracy of identified model.
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Linear regression model with autocorrelated residuals
Kostka, Ján ; Zichová, Jitka (advisor) ; Hudecová, Šárka (referee)
The aim of this bachelor thesis is to introduce the algorithm for analysis of the linear regression model with autocorrelated residuals, which is applicable to time series data. For residuals, we assume the ARMA model, eventually ARIMA model, which enlarges the possibilities of application. The analysis of such regression models includes detection of autocorrelation and related tests, detection of stationarity and related unit root test, followed by model identification for residuals and maximum likelihood estimation of identified regression model.
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Models of binary time series
Kunayová, Monika ; Zichová, Jitka (advisor) ; Cipra, Tomáš (referee)
This bachelor thesis deals with the time series of binary variables that exist in many social spheres. The indicator may denote a certain value being exceeded or a phenomenon occurring. We study a model of logistic autoregression and its properties, partial likelihood function which allows us to work with dependent data, and derive useful relationships for a practical application that consists of time series simulation and real data analysis using free software R.
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Recursive estimates of financial time series
Vejmělka, Petr ; Cipra, Tomáš (advisor) ; Zichová, Jitka (referee)
This work aims to describe the method of recursive estimation of time series with conditional volatility, used mainly in finance. First, there are described the basic types of models with conditional heteroskedasticity (GARCH) and princi- ples of state-space modeling demonstrated by means of linear models AR and ARMA. Subsequently, there are derived algorithms for recursive estimation of parameters of the GARCH model and its possible modifications including the ones for which recursive estimation formulas have not been yet derived in lit- erature. These algorithms are tested in a simulation study, where their appli- cability in practice is investigated. Finally, we apply these algorithms to real high-frequency data from the stock exchange. The practical part is done us- ing the software Mathematica 11.3. The work also serves as an overview of the current state of online modeling of financial time series. 1
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