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Demonstrational programs for music record processing
Jonáš, Petr ; Rajmic, Pavel (referee) ; Číž, Radim (advisor)
This bachelor’s thesis describes the processing of music records and signals. Demonstration programs were created in Matlab. In this thesis were created function of equalization, transposition and sound effects. In this thesis was created application for determining the similarity of signals. For both programs was created graphic user interface.
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Demonstrational programs for music record processing
Jonáš, Petr ; Rajmic, Pavel (referee) ; Číž, Radim (advisor)
This bachelor’s thesis describes the processing of music records and signals. Demonstration programs were created in Matlab. In this thesis were created function of equalization, transposition and sound effects. In this thesis was created application for determining the similarity of signals. For both programs was created graphic user interface.
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Hypotheses Testing in Financial Time Series
Kubů, Jan ; Zichová, Jitka (advisor) ; Jonáš, Petr (referee)
Financial data often take the form of time series. In such cases, their analysis is performed using statistical methods for time series. The thesis describes selected parametric and nonparametric tests of random walk hypothesis. Tests are designed against common mutual correlation alternatives but also against trend and cyclic data structure alternatives. The thesis provides the theoretical basis of these tests and their application to real financial data.
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Seasonality and periodicity in time series
Musil, Karel ; Jonáš, Petr (advisor) ; Cipra, Tomáš (referee)
This work deals with periodicity and seasonality in time series. After a time series periodicity topic is introduced, a seasonal component of time series and a seasonal adjustment is presented. Then basic approaches, used in current practice, are introduced. These are classic model approach, Box-Jenkins methodology, and spectral analysis. The described seasonal adjustment techniques are applied to the time series of the Czech import, export, and foreign trade balance. A brief description of potential problems, which are connected to the seasonal adjustment and are common in practice, is a part of the example as well.
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Models of integer-valued time series
Vagaský, Ján ; Prášková, Zuzana (advisor) ; Jonáš, Petr (referee)
In this thesis models of integer-valued time series based on random sums of random variables are studied. We describe basic properties of a simple branching process, an INAR(1) process and a first- order binomial autoregresive process. We prove the Markov property of each of these processes and study conditions required for the processes to be weak-stationary. Using generating functions of random variables we derive moments and cumulants up to the fourth order for INAR(1) process and binomial AR(1) process. Powered by TCPDF (www.tcpdf.org)
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Robust classification and discrimination
Rensová, Dita ; Kalina, Jan (advisor) ; Jonáš, Petr (referee)
This thesis is focused on classification methods and their robust alternatives. First, we recall the standard classification rules of linear and quadratic discrim- ination analysis. We also show some methods for estimating their probability of missclassification. Next we describe some existing robust multivariate estimators, their properties and computational algorithms. These estimators are consequently used to construct robust classification rules. Then, we describe the principal com- ponent analysis as a technique for dimension reduction. Again, we study methods for its robustification. Finally, we illustrate the usage of robust classification on both numerical simulations and real data. We also investigate the influence of the principal component analysis on classification results.
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Hypotheses Testing in Financial Time Series
Kubů, Jan ; Zichová, Jitka (advisor) ; Jonáš, Petr (referee)
Financial data often take the form of time series. In such cases, their analysis is performed using statistical methods for time series. The thesis describes selected parametric and nonparametric tests of random walk hypothesis. Tests are designed against common mutual correlation alternatives but also against trend and cyclic data structure alternatives. The thesis provides the theoretical basis of these tests and their application to real financial data.
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Seasonality and periodicity in time series
Musil, Karel ; Jonáš, Petr (advisor) ; Cipra, Tomáš (referee)
This work deals with periodicity and seasonality in time series. After a time series periodicity topic is introduced, a seasonal component of time series and a seasonal adjustment is presented. Then basic approaches, used in current practice, are introduced. These are classic model approach, Box-Jenkins methodology, and spectral analysis. The described seasonal adjustment techniques are applied to the time series of the Czech import, export, and foreign trade balance. A brief description of potential problems, which are connected to the seasonal adjustment and are common in practice, is a part of the example as well.
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Vector Autoregressive Models
Jonáš, Petr ; Lachout, Petr (referee) ; Cipra, Tomáš (advisor)
In the presented work vector autoregression (VAR) models of finite order are examined. The main part is concerned with stationary VAR processes, whose basic characteristics, various methods of coefficient matrices estimation including consistency conditions are derived. We discuss the point and interval forecasts based on VAR models as well. We also describe integrated processes, principle of cointegration and VEC models which are appropriate modifications of VAR models for cointegration processes. The work also pays attention to Granger's and multi-step causality in the context of VAR models. In the final chapter impulse response analysis and forecast error variance decomposition are presented. Everything is supplemented by illustrative examples on real data.
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