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Efficient implementation of methods for the restoration of damaged audio signals
Csiba, Hajnalka ; Rajmic, Pavel (referee) ; Mokrý, Ondřej (advisor)
This bachelor's thesis deals with the restoration of audio signals containing unknown samples at known locations using two algorithms. The first is the Janssen algorithm and the second is a method based on non-negative matrix factorization. Janssen algorithm is built on the principle of the autoregressive model. The restoration of the samples is performed in such a way that the restored signal matches the predicted model as precisely as possible. The algorithm based on non-negative matrix factorization is used to decompose the frequency spectrogram of the signal as the product of non-negative matrices.
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Financial time series modelling with trend
Studnička, Václav ; Zichová, Jitka (advisor) ; Prášková, Zuzana (referee)
Various models can be used for the analysis of financial time series. This thesis focuses mainly on two models; non-linear trend model and linear trend model. First chapter is theoretial, there is an introduction to the theory of time series and to the autoregressive process. Second chapter is also theoretical and it focuses on a description of both non-linear and linear trend model including derivations of im- portant properties of these models; moreover, it contains theory for the modelling of financial time series and predictions. Last chapter contains simulations of two mentioned models and estimations of their parameters, Wolfram Mathematica is used for all simulations. 1
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Financial time series modelling with trend
Studnička, Václav ; Zichová, Jitka (advisor) ; Prášková, Zuzana (referee)
Various models can be used for the analysis of financial time series. This thesis focuses mainly on two models; non-linear trend model and linear trend model. First chapter is theoretial, there is an introduction to the theory of time series and to the autoregressive process. Second chapter is also theoretical and it focuses on a description of both non-linear and linear trend model including derivations of im- portant properties of these models; moreover, it contains theory for the modelling of financial time series and predictions. Last chapter contains simulations of two mentioned models and estimations of their parameters, Wolfram Mathematica is used for all simulations. 1
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Selected Unit Root Tests in Time series
Fedorová, Darina ; Arltová, Markéta (advisor) ; Hindls, Richard (referee)
The emphasis of this diploma thesis is placed on the verification of stationarity in time series using the Unit Root Tests and their most common modifications that are introduced in the theoretical part of this paper. Tests mainly by Dickey and Fuller, Phillips and Perron, and KPSS test are introduced as well as their modifications in the form of ERS, Ng and Perron, and Leybourne and McCabe tests. Moreover the HEGY test for testing stationarity in the seasonal Time series and Perron test of structural breaks for Time series with shocks are described. There is also outlined the process of testing multiple Unit Roots. The empirical part of this paper consists of simulations of AR(1) time series generated using the software R, their testing for stationarity by selected Unit Root tests and the comparison of power of these tests. The conclusion includes recommendations which tests and under what conditions are the most suitable for testing Time series for the presence of Unit Root.
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