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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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Recursive estimates of financial time series
Vejmělka, Petr ; Cipra, Tomáš (advisor)
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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Recursive estimates of financial time series
Vejmělka, Petr ; Cipra, Tomáš (advisor)
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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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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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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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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