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Impulse noise detection in audio signals
Hůla, Josef ; Ištvánek, Matěj (referee) ; Mokrý, Ondřej (advisor)
Study disserts known method of detecting impulsive noise in audiosignal. Differential, filtering, autoregressive and ARMA methods are discussed. First, each method is theoretically examined and the character of impulsive disturbances is presented. Later an~implementation of each method is presented and results of their performance is compared. In order to have comparable results, the methods are tested on synthetic impulses with known position and duration and also on recordings containing real impulsive noise.
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Impulse noise detection in audio signals
Hůla, Josef ; Ištvánek, Matěj (referee) ; Mokrý, Ondřej (advisor)
Study disserts known method of detecting impulsive noise in audiosignal. Differential, filtering, autoregressive and ARMA methods are discussed. First, each method is theoretically examined and the character of impulsive disturbances is presented. Later an~implementation of each method is presented and results of their performance is compared. In order to have comparable results, the methods are tested on synthetic impulses with known position and duration and also on recordings containing real impulsive noise.
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Tests of significance of ARMA models parameters based on Bayesian approach
Onderko, Martin ; Krtek, Jiří (advisor) ; Prášková, Zuzana (referee)
This thesis is focused on Bayesian analysis and its use in probability and statistics. It also marginally discusses random processes, furtherly describes ARMA model and defines the issue of estimation of the parameters of Bayesian approach. Acquired knowledge and derived characteristics subsequently applies in testing of significance of parameters. Thus it undoubtably affects the area of hypothesis testing and serves mainly as a tool to determine the ARMA model more accurately. This work should be regulary applied when detecting the necessity of testing of statistical significance of parameters of ARMA model.
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Financial time series model identification
Fučík, Jan ; Zichová, Jitka (advisor) ; Prášková, Zuzana (referee)
This thesis deals with the financial time series model identification. The univariate and multivariate ARMA models and their identification criteria are described. The procedures using the correlation structure of the time series and some information criteria are presented. The functioning of the criteria is verified on simulated time series AR, MA and ARMA. Afterwards, the criteria are compared in terms of reliability and simplicity of use. Finally, there are two examples of univariate and multivariate ARMA model identification for the real financial time series. The data and the R programme source code are enclosed on a CD. Powered by TCPDF (www.tcpdf.org)
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Time series models with exogenous variables and their application to economical data
Vaverová, Jana ; Zichová, Jitka (advisor) ; Cipra, Tomáš (referee)
This thesis deals with analyzing multivariate financial and economical data. The first section describes the theory of multivariate time series and multivariate ARMA models. The second part deals with some models with exogenous variables such as simultaneous equations models and ARMAX model. In the final chapter, the described theory is applied to analyze the reciprocal dependence of time series of inflation rates and dependence of inflation rates on various macroeconomical indicators. The results were obtained by software Mathematica 8, Mathematica 10, EViews and R. Powered by TCPDF (www.tcpdf.org)
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Nonlinear ARMA model
Šabata, Marek ; Lachout, Petr (advisor) ; Prášková, Zuzana (referee)
The thesis regards theory of nonlinear ARMA models and its application on financial mar- kets data. First of all, we present general framework of time series modeling. Afterwards the theory of linear ARMA models is layed out, since it plays a key role in the theory of nonlinear models as well. The nonlinear models presented are threshold autoregressive model (TAR), autoregressive conditional heteroscedastic model (ARCH) and generalized autoregressive conditional heteroscedastic model (GARCH). For each model, we derive a method for esti- mating the model's parameters, asymptotic properties of the estimators and consequently confidence regions and intervals for testing hypotheses about the parameters. The theory is then applied on financial data, speficically on the data from Standard and Poor's 500 index (S&P500). All models are implemented in statistical software R. 1
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Tests of significance of ARMA models parameters based on Bayesian approach
Onderko, Martin ; Krtek, Jiří (advisor) ; Prášková, Zuzana (referee)
This thesis is focused on Bayesian analysis and its use in probability and statistics. It also marginally discusses random processes, furtherly describes ARMA model and defines the issue of estimation of the parameters of Bayesian approach. Acquired knowledge and derived characteristics subsequently applies in testing of significance of parameters. Thus it undoubtably affects the area of hypothesis testing and serves mainly as a tool to determine the ARMA model more accurately. This work should be regulary applied when detecting the necessity of testing of statistical significance of parameters of ARMA model.
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