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Tests of independence between two time series
Zdeněk, Pavel ; Pawlas, Zbyněk (advisor) ; Prášková, Zuzana (referee)
The goal of this diploma thesis is to introduce several tests of independence for time series following the ARMA model and then compare them within the simulation study. First, the basic theory of independence is reminded together with covariance and corre- lation. Asymptotic unbiasedness and consistency are derived for sample cross-covariance and also consistency for correlation. After the introduction of the ARMA model, each test is described and its advantages and disadvantages discussed. The following tests are included: Haugh test, using estimates of white noise and sample cross-correlation, modi- fied t-test, for which we assume weakly stationary series instead of random samples, and lastly distance covariance test, which uses properties of characteristic functions. These tests are compared in the simulation study together with the standard independence test using Pearson correlation coefficient. At the end, an illustrative example with finance data is presented. 1
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Multivariate volatility forecasts for large portfolios
Vágner, Jan ; Cipra, Tomáš (advisor) ; Prášková, Zuzana (referee)
One deals with the estimation and consequent forecast of the integrated covariance matrix in the context of high-frequency stock price data and high dimensionality regarding the number of analyzed assets. We present several methods for the integrated covariance estimation and then use these estimates as a basis for forecasting models. We mainly focus on the multivariate extensions of the HAR model. Finally, in the empirical study, we compare different model-estimator combinations (based on 5-min interval observation and 50 assets) using economic and statistical evaluation. Economic evaluation is based on portfolio optimization, including transaction costs. 1
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Nonlinearity detection in financial time series
Dudlák, Oliver ; Zichová, Jitka (advisor) ; Prášková, Zuzana (referee)
The aim of this master thesis is nonparametric and parametric nonlinearity testing in time series and its application on real financial data. From nonparametric tests, we describe a bispectral density test. Based on it, we can test symmetry and linearity of observed time series. Because of complex nature of the test we included the theory of complex random variable. From parametric tests, we introduce the RESET test and its modifications, Keenan test and F test. Considering the analogy between these tests and the test for submodel in linear model, we included basic theory of linear model and multivariate linear regression model. For both cases we performed a simulation study, where we observe frequencies of rejections of null hypothesis in both linear and nonlinear time series. When we get frequencies corresponding to the theoretical significance levels of the test, statistics we continue analyzing the real data.
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Creation and application of the system of assessing the financial situation of the company
PRÁŠKOVÁ, Zuzana
The principal objective of this thesis is to create a suitable evaluation system of financial and economic evaluation of the company RM Chemicals s. r. o. based on data obtained from the financial statements for previous five years. Subsequently, the developed system will be applied and ascertained data with regard to the further development of the company will be evaluated. This thesis contains theoretical bases describing what the financial analysis is, what are the sources of information, which methods are used and who the users in financial analysis are. This thesis also deals with calculating the indicators and required to determinate the financial situation of the company such as absolute indicators of liquidity, profitability, activity or indebtedness, differential and proportion indicators or bankruptcy and creditworthy models. This analysis is used to improve financial situation of the company. The last part shows the results and some recommendations which indicators and methods of financial analysis should be used in the future.
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Alternative estimators for ARMA-GARCH models
Mašát, Filip ; Hudecová, Šárka (advisor) ; Prášková, Zuzana (referee)
GARCH models are used to describe the volatility of time series. GARCH processes are usually estimated by maximum likelihood or by maximum quasi-likelihood method. However, as these methods require knowledge of the distribution of the innovations or the existence of their fourth moment, they are not always suitable. Several alternative methods that could be an appropriate alternative to classical estimators are described in this thesis. Those estimators are: least squares estimators, weighted Lp estimators and least absolute deviations estimator with logarithmic transformation. These estimators are compared in a simulation study for various settings. A real data application is provided as well. 1
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Vector autoregression
Jelenčiak, Jakub ; Cipra, Tomáš (advisor) ; Prášková, Zuzana (referee)
Vector autoregression model VAR belongs to the most used multiple time series models mainly in field of financial econometrics. The main role of this text is to survey basic theory of VAR models and to illustrate application of theory on real data. At first the properties of multiple time series and basic linear models are described. Then we focus on the VAR model, more specifically on its description, construction and application. In the construction subsection our primary focus is on the order identification, model estimation by OLS method and diagnostics. In the diagnostics basic assumptions of the model are checked, more specifically stationarity, correlation of the residuals and normality. In applications we focus on explanation and description of Granger causality. In the last section previously described theory is applicated on real data in two examples. On them we illustrate construction of the VAR model. Furthermore, in the second example we also analyze causality and discuss the results. 1
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Multivariate ARCH and GARCH models
Šafránková, Jana ; Prášková, Zuzana (advisor) ; Hurt, Jan (referee)
We study multivariate ARCH and GARCH models and their subsequent application to simulated and real data. In discussed models the conditional variance matrix is considered to be a function of lagged data process which is the subject of study. In case of GARCH models the conditional variance matrix is dependent on own lagged values, too. First of all, we deal with univariate ARCH and GARCH models to get some theoretical basis. The subsequent study extends this basis to multivariate models. A survey of multivariate GARCH models is presented in the next part of this thesis. Further study is devoted to maximum likelihood estimators of these models and we deal with alternatives to multivariate normal distribution which is a standard assumption of this method. We occupy ourselves with tests of these models, too. We mention both preestimation tests and postestimation tests to verify the adequacy of models. In conclusion we give practical examples which show di±culties of applications of these models for real data.
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Special problems of non-stationarity in financial time series
Radič, Pavol ; Zichová, Jitka (advisor) ; Prášková, Zuzana (referee)
The aim of this thesis is a detailed analysis of selected approaches of unit root testing. First chapter deals with the basic knowledge of the theory of stochastic processes. Further, we describe Dickey-Fuller tests, t-tests and likelihood ratio tests for the presence of a unit root and derive their asymptotic properties. Numerical studies include comparison of accuracy of the parameter estimates, estimating quantiles of the presented distributions, their graphical presentation and determination of power of our tests. The acquired theoretical knowledge is applied on real data which were analyzed using software Mathematica and R. Powered by TCPDF (www.tcpdf.org)
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