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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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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
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Multivariate models of volatility
Vejmělka, Petr ; Cipra, Tomáš (advisor) ; Zichová, Jitka (referee)
In this work, we deal with the modeling of multivariate financial time series. First, linear models of multivariate time series are described and further special features of the financial time series. In the next part of the thesis, we focus on modeling multivariate volatility and present several models that can be used in this context. In the practical part of the work, we apply some of these models on real data using the software systems EViews 9 and RATS 8. As the first one, we analyze gradually two-dimensional and five-dimensional financial time series. The aim of thesis is to survey the temporary state of multivariate volatility modeling in financial time series including practical experience with specialized software. 1
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Korelační analýza akciových indexů pomocí Empirical Mode Decomposition
Ulyanin, Alexey ; Černý, Michal (advisor) ; Formánek, Tomáš (referee)
This thesis studies dependence of ?nancial time series, represented by stock indices of geographically separated economics. Daily prices of selected stock indices from 01.05.1988 to 20.04.2017 are used for the analysis. In the fi?rst section the dataset is described. The second section goes through methodology for the analysis, including empirical mode decomposition (EMD) algorithm, with the help of which the initial time series can be transformed into a few time series, that are mostly independent on each other, for further analysis (for example, correlation analysis). EMD is an interesting method of signal processing, which may help to look at the time series analysis from a different perspective. The thesis should extend the work of Guhathakurta et al. (2008) and extend the time scale and number of indices. Correlation analysis is also performed on the initial time series and the transformed ones. The aim of this thesis is to prove, whether stock indices of geographically separated economics have similarities in their behavior and test whether they are dependent on each other, by using methods from Guhathakurta et al. (2008) extended by correlation analysis.
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Volatility models in R
Vágner, Hubert ; Bašta, Milan (advisor) ; Flimmel, Samuel (referee)
This diploma thesis focuses on modeling volatility in financial time series. The main approach to modelling volatility is using GARCH models which can capture the variability of conditional volatility of time series. For modelling a conditional mean value in time series are used ARMA models. In the series there are usually not fulfilled the assumption of earnings normality, therefore, are the earnings in most cased characterized by the leptokurtic shape of distribution. The thesis introduces some more distribution types, which can be more easily used for the earnings distribution - above all the Students t distribution. The aim of the thesis in the first part is to present the topic of financial time series and description of the GARCH models including their further modification. There are used e.g. IGARCH or other models capturing asymmetric impact of shocks such as GJR-GARCH. The second part deals with generated data, where are more in detail explored the volatility models and their behavior in corresponding financial time series. The third part focuses on the volatility estimation and forecasting for the financial time series. Firstly this concerns development of stock index MICEX secondly currency pair Russian Ruble to Czech Crown and eventually price development of the Brent crude oil. The goal of the third part is to present the impacts on volatility of chosen time series applied on the example of economic sanctions against Russia after annexation of the Crimea peninsula which happened in the first quarter 2014.
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Selected problems of financial time series modelling
Hendrych, Radek ; Cipra, Tomáš (advisor) ; Arlt, Josef (referee) ; Prášková, Zuzana (referee)
Title: Selected problems of financial time series modelling Author: Radek Hendrych Department: Department of Probability and Mathematical Statistics (DPMS) Supervisor: Prof. RNDr. Tomáš Cipra, DrSc., DPMS Abstract: The present dissertation thesis deals with selected problems of financial time series analysis. In particular, it focuses on two fundamental aspects of condi- tional heteroscedasticity modelling. The first part of the thesis introduces and discusses self-weighted recursive estimation algorithms for several classic univariate conditional heteroscedasticity models, namely for the ARCH, GARCH, RiskMetrics EWMA, and GJR-GARCH processes. Their numerical capabilities are demonstrated by Monte Carlo experiments and real data examples. The second part of the thesis proposes a novel approach to conditional covariance (correlation) modelling. The suggested modelling technique has been inspired by the essential idea of the multivariate orthogonal GARCH method. It is based on a suitable type of linear time-varying orthogonal transformation, which enables to employ the constant conditional correlation scheme. The correspond- ing model is implemented by using a nonlinear discrete-time state space representation. The proposed approach is compared with other commonly applied models. It demon- strates its...
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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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MCMC methods for financial time series
Tritová, Hana ; Pawlas, Zbyněk (advisor) ; Komárek, Arnošt (referee)
This thesis focuses on estimating parameters of appropriate model for daily returns using the Markov Chain Monte Carlo method (MCMC) and Bayesian statistics. We describe MCMC methods, such as Gibbs sampling and Metropolis- Hastings algorithm and their basic properties. After that, we introduce different financial models. Particularly we focus on the lognormal autoregressive model. Later we theoretically apply Gibbs sampling to lognormal autoregressive model using principles of Bayesian statistics. Afterwards, we analyze procedu- res, that we used in simulations of posterior distribution using Gibbs sampling. Finally, we present processed output of both simulated and real data analysis.
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Some modifications of models ARCH for financial time series
Nekvinda, Matěj ; Cipra, Tomáš (advisor) ; Zichová, Jitka (referee)
This work deals with modelling time series, especially their volatility, by methods based on the ARCH model. In the beginning, we describe the general features of financial time series, afterwards we focus on the ARCH model modifications. The described modifications are GARCH, EGARCH, GJR-GARCH and briefly GARCH-M, IGARCH, FIGARCH and QGARCH. Along with the models, there is a description of their behaviour, which frequently reflects some features of financial time series. We also mention the process of practical financial time series analysis. In the end, we demonstrate the application of GARCH, EGARCH and GJR-GARCH models for modelling values of FTSE 100 index together with diagnostic tests and prediction. Powered by TCPDF (www.tcpdf.org)
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Product processes as a tool for financial analysis
Krejčí, Kateřina ; Zichová, Jitka (advisor) ; Hurt, Jan (referee)
This bachelor thesis discusses product processes as a tool for modeling financial time series. The thesis is divided into the theoretical and the practical part. Basic issues are summarized in the theoretical part. Properties of some moments and correlations are described and derived in this part, parameter estimates of a product process are derived subsequently. The practical part deals further with the parameter estimates. The quality of derived parameter estimates is verified in a simulation study in software Mathematica 9 and the proposed estimates are applied to real financial data. Powered by TCPDF (www.tcpdf.org)
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