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Multivariate volatility models
Šimjáková, Dominika ; Cipra, Tomáš (referee) ; Zichová, Jitka (advisor)
The subject of the thesis is the analysis of univariate and multivariate time series. The GARCH models as well as the the simpli cated ARCH models are described in detail. In the practical part of the master thesis are elaborated some time series of exchange rates. The aim of this work is to nd an appropriate model which would reliably aproximate the development of the series. The exchange rates time series were analyzed by the software XploRe and Eviews. The data and programme source code are enclosed on a CD.
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Nonparametric models of financial time series
Pazdera, Jaroslav ; Cipra, Tomáš (referee) ; Prášková, Zuzana (advisor)
In this diploma thesis we study basic models of time series, both parametric and nonparametric, and their basic properties. In the first part several conditional homoscedastic models are examined and the basic estimation methods are explained. Afterwards, we continue with conditional heteroscedastic models. We explain the reasons why are these models suitable to analyze financial time series. We state and prove the conditions for the strict stationarity of GARCH and calculate the mean square error (MSE) of prediction in GARCH(1,1). Eventually, the robustness of the least absolute deviation (LAD) method for GARCH is discussed and supported by numerical results. At the end of this thesis we discuss methods for nonparametric GARCH(1,1) estimation.
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Discrete and limited dependent variables in econometrics
Bejda, Přemysl ; Prášková, Zuzana (referee) ; Cipra, Tomáš (advisor)
In the present work we study discrete and limited dependent variables. We begin with binary dependent variables. Then we show an example, where we use the data from psychological area. We work with econometric software EViews and show its possibilities, which are connected with our subject of study. We write procedures for "jackknife" method and simple random sample, compare logit, probit and gompit models and draw a graph of conditional probability of our models. Likewise we work with ordinal dependent variables. We use the same data as in the previous example. It means that we investigate possibilities of EViews and add some procedures for "jackkni ng," simple random sampling and for drawing pictures of conditional probability. Just from theoretical point of view we consider unordered dependent variables. In the next chapter we focus on limited dependent variables. We show theory of censored and truncated explained variables. As an application we show theory of survival analysis, which is used in our last example. Statistical computing is performed in R, because no suitable methods are implemented in EViews.
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Selected topics of multivariate time series analysis in finance
Slívová, Iveta ; Cipra, Tomáš (referee) ; Zichová, Jitka (advisor)
In the present work, we study ARMA model at the beginning, then we write about one-dimensional and multivariate ARCH and GARCH model, further we move on to the multivariate GARCH model. At the end, the principal component decomposition is introduced, it is a procedure to reduce the number of parameters involved in a multivariate GARCH model. The theory is explicated rst on a basic ARMA model, afterwards it is modi ed step by step for the one-dimensional and the multivariate GARCH model. There are solved examples for multivariate ARCH and GARCH model and nancial data are analyzed by means of these models.
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Dynamic analysis of portfolio by means of Kalman filter
Králová, Dana ; Hanzák, Tomáš (referee) ; Cipra, Tomáš (advisor)
The aim of the presented work is to introduce the new method of dynamic analysis of portfolio which estimates the composition of portfolio on the base of its returns. In the work, we describe the theory of Kalman filter and state space models. We mention examples of application of Kalman filter and demonstrate the work with econometric software EViews in the field of state space models on this examples. We deal with selected aspects from the portfolio theory. We present the older method of analysis of portfolio which uses the regression model and we draw attention to its essential lack. We deal, in more details, with the method of dynamic analysis of portfolio which is based on the state space models and which removes the lack of the older method. We also study the modification of this method for hedge funds. In the end, we apply the method of dynamic analysis of portfolio on the real data of two Czech investment funds and so we verify the quality of the model.
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Econometric systems of simultaneous equations in life insurance
Hendrych, Radek ; Prášková, Zuzana (referee) ; Cipra, Tomáš (advisor)
In present work we deal with theoretical and practical issues related to econometric systems of (linear) simultaneous equations. In the first chapter we introduce to theoretical aspects of this problem. We devote considerable space to estimation procedures and comparisons of their properties, mention questions of identification, an inconsistency of OLS-estimates for the simultaneous modeling, tests of hypotheses specific to this area, dynamic systems and constructions of forecasts in models. In the second chapter we introduce selected basic concepts relevant to life insurance. In the third chapter we show the practical application of theoretical knowledge in the event of an econometric model of financial flows in the life insurance company operating on the Czech market. We compare ordinary estimation procedures (2SLS and 3SLS approach), perform some tests, which serve us to verify selected information on the studied model. We show the possibility of using residual bootstrap, including examples of use in the construction of confidence intervals. Finally we analyze several predictions of the estimated model of the life insurance company for predetermined scenarios for the development of selected variables, which is very important from practical point of view.
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Modelling financial time series
Holubářová, Šárka ; Cipra, Tomáš (referee) ; Zichová, Jitka (advisor)
This diploma thesis deals with modelling nancial time series and especially the changing volatility of nancial returns, which is characteristic for them. The theoretical part of the thesis describes several processes with non-constant conditional variance, which form an alternative to the classical ARMA approach to modelling time series. The focus is mainly on two types of processes - lognormal autoregressive process for conditional variance as an example of process where the conditional variance is independent of past returns, and on ARCH processes which to the contrary are based on dependence of the conditional variance on past returns. The properties of described models are veri ed and demonstrated in a simulation study carried out in Mathematica. Final part of the thesis is dedicated to application of the models to real data and modelling volatility of time series of returns of shares and currency rates. The parameters of the models are estimated and forecasts calculated in Mathematica with partial use of programme XploRe.
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