
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


Risk aggregation allowing for skewness
Šimonová, Soňa ; Mazurová, Lucie (advisor) ; Zichová, Jitka (referee)
The main objective of this thesis is to examine different methods of calcula tion of economic capital for an insurance company which allow for skewness. For calculating the economic capital we use two alternative risk measures Value at Risk (VaR) and Conditional Value at Risk (CVaR). The first part of the thesis is concerned with deriving exact formulae for VaR and CVaR for normally distribu ted losses and describing the modification of these formulae using CornishFisher approximation. Next, the method using lognormal model with a parameter cap turing skewness is discussed. The parameter is used for deriving a formula for skewness of a sum of losses. The approximation of the sum is thus obtained and is used for deriving formulae for VaR and CVaR for aggregated losses. Finally, the methods are compared numerically using R software. 1


Parametric Nonlinearity Testing in Time Series
Kollárová, Dominika ; Zichová, Jitka (advisor) ; Cipra, Tomáš (referee)
The aim of this bachelor thesis is the theoretical description of the functioning of two parametric nonlinearity tests  the RESET test and Keenan's test and theirs application on financial time series with the summary of achieved results. During the testing we assume, that a time series follows a predetermined linear AR(p) model the order of which is identified by the partial autocorrelation function or the AIC criterion.


Composite distributions of loss sizes
Karatun, Ksenia ; Mazurová, Lucie (advisor) ; Zichová, Jitka (referee)
In this work, we deal with composite distributions that can be used to model loss sizes in some specific classes of nonlife insurance. The first part contains definition of the general composite model and its special features. The second part describes models that are made up by piecing together Weibull distribution and distributions belonging to a family of transformed beta distributions. The third part describes algorithm that computes the maximum likelihood estimators for parameters of composite distribution and criteria of the relative quality of statistical models. In the last part we apply composite models to two real data sets. 1


Linear and nonlinear autoregressive models for time series from economics and finance
Cvetković, Jelena ; Zichová, Jitka (advisor) ; Hendrych, Radek (referee)
This bachelor thesis deals with linear and nonlinear autoregressive models for time series from economics and finance. It consists of theoretical and practical part. In theoretical part, the reader acquaints with terms connected to random proces ses; then autoregressive and threshold autoregressive time series are introduced, their general properties are derived, possible ways of forecasting are described and ways of parameters estimation are presented. Furthermore, test for threshold autoregression is introduced. The practical part is divided into simulation study, where the quality of estimations and the power of the test is examined on simu lated time series, and into application on real data, where the acquired findings are utilized on time series of share prices of the company ČEZ. 1
