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ARFIMA time series models
Vdovičenko, Martin ; Hudecová, Šárka (advisor) ; Prášková, Zuzana (referee)
The thesis deal with long-memory processes which are defined by several ways. The main concern is dedicated to ARFIMA model, to its basic properties and its application. Next, graphical, semiparametric and parametric estimation methods of ARFIMA parameters are described in detail. Five selected R packages are introduced that are suitable for modeling long-memory processes. We discuss their basic functions with description of input arguments and output. Finally, the application of the packages on real data is discussed according to results of~each function. Data sample comes from the Nile River and represents its yearly minimal water levels. Powered by TCPDF (www.tcpdf.org)
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Testing time-series characteristics of prices of financial derivatives
Vdovičenko, Martin ; Kadavý, Matěj (advisor) ; Šnupárková, Jana (referee)
This work discusses Brownian motion and its basic transformations. The work describes basic properties of its trajectories and shows that Brownian motion is a martingale and a self-similar process. Next, we discuss time series analysis. We introduce graphical tools for analyzing data and we describe theoretical basics of some normality and independence tests. Finally, we consider the hypothesis that in the short run the price of financial assets can be modelled by Brownian motion. We conduct basic statistical tests on real data using the R progam and we talk through our results.
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ARFIMA time series models
Vdovičenko, Martin ; Hudecová, Šárka (advisor) ; Prášková, Zuzana (referee)
The thesis deal with long-memory processes which are defined by several ways. The main concern is dedicated to ARFIMA model, to its basic properties and its application. Next, graphical, semiparametric and parametric estimation methods of ARFIMA parameters are described in detail. Five selected R packages are introduced that are suitable for modeling long-memory processes. We discuss their basic functions with description of input arguments and output. Finally, the application of the packages on real data is discussed according to results of~each function. Data sample comes from the Nile River and represents its yearly minimal water levels. Powered by TCPDF (www.tcpdf.org)
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Testing time-series characteristics of prices of financial derivatives
Vdovičenko, Martin ; Kadavý, Matěj (advisor) ; Šnupárková, Jana (referee)
This work discusses Brownian motion and its basic transformations. The work describes basic properties of its trajectories and shows that Brownian motion is a martingale and a self-similar process. Next, we discuss time series analysis. We introduce graphical tools for analyzing data and we describe theoretical basics of some normality and independence tests. Finally, we consider the hypothesis that in the short run the price of financial assets can be modelled by Brownian motion. We conduct basic statistical tests on real data using the R progam and we talk through our results.
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