
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 firstorder FIGARCH model.


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 nonconstant 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


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.


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 ChainLadder method, the basic method for forecasting outstanding claims, and then it's extention to Double ChainLadder 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


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 Qtests and BDStest. 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.


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.


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.


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 statespace 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 highfrequency 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


Seasonal mortality and its application in life insurance
Srnáková, Andrea ; Cipra, Tomáš (advisor) ; Zichová, Jitka (referee)
Assumptions like uniform distribution, constant force of mortality and the Balducci assumption frequently used for modeling mortality data do not reflect the variability of monthly death rates. Often a phenomenon of winter excess mortality occurs, which is not respected by these assumptions. We shall apply a seasonal mortality assumption, which uses nonnegative trigonometric sums for modeling the distribution of monthly death rates. We then apply our findings to the Czech mortality data. We calculate monthly premiums in a shortterm life insurance policy and compare the result with results given by the classical assumptions. 1


Claims reserve volatility and bootstrap with aplication on historical data with trend in claims development
Malíková, Kateřina ; Pešta, Michal (advisor) ; Zichová, Jitka (referee)
This thesis deals with the application of stochastic claims reserving methods to given data with some trends in claims development. It describes the chain ladder method and the generalized linear models as its stochastic framework. Some simple functions are suggested for smoothing the origin and development period coefficients from the estimated model. The extrapolation is also considered for estimation of the unobserved tail values. The residual bootstrap is used for the reparameterized model in order to get the predictive distribution of the estimated reserve together with its standard deviation as a measure of volatility. Solvency capital requirement in one year time horizon is also calculated. 1
