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Evaluation of Methods for AR Coefficients Estimation Using Monte Carlo Analysis
Klejmova, Eva
Aim of this paper is to give recommendation for work with methods used for estimation of coefficients of autoregressive process. We applied Monte Carlo simulations to investigate performance of Burg, Yule-Walker and covariance methods. Evaluation of precision of spectral estimation is done with focus on signal length and lag order. The results are presented in graphical form and briefly discussed. Taking these results into account, Yule-Walker method shows better performance in case of long length signals and in case of overvalued lag order. Burg and covariance methods provide better results in case of short length signal and undervalued lag order.
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Selected Aspects of Statistical Significance Testing in Time-Frequency Analysis
Klejmová, Eva ; Kohl,, Zdeněk (referee) ; Fidrmuc, Jarko (referee) ; Poměnková, Jitka (advisor)
Přeložená dizertační práce se zabývá analýzou a posouzením kvality odhadu frekvenční a časově-frekvenční transformace dat a formulaci doporučení pro práci s metodami. Při použití těchto metod vyvstává otázka, jak vyhodnotit, které složky spektrogramu jsou statisticky významné a které nikoli. V této práci analyzujeme vlastnosti standardních testů statistické významnosti. Diskutujeme o jejich výhodách a nevýhodách s ohledem na heteroskedastický charakter dat. Na základě našich experimentů jsou v práci navrženy dva typy testovacích metod, které snižují negativní aspekty standardních testů. Práce jen zakončena vytvořením rámce pro filtrování dat pomocí námi navržených metod.
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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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Selected Aspects of Statistical Significance Testing in Time-Frequency Analysis
Klejmová, Eva ; Kohl,, Zdeněk (referee) ; Fidrmuc, Jarko (referee) ; Poměnková, Jitka (advisor)
Přeložená dizertační práce se zabývá analýzou a posouzením kvality odhadu frekvenční a časově-frekvenční transformace dat a formulaci doporučení pro práci s metodami. Při použití těchto metod vyvstává otázka, jak vyhodnotit, které složky spektrogramu jsou statisticky významné a které nikoli. V této práci analyzujeme vlastnosti standardních testů statistické významnosti. Diskutujeme o jejich výhodách a nevýhodách s ohledem na heteroskedastický charakter dat. Na základě našich experimentů jsou v práci navrženy dva typy testovacích metod, které snižují negativní aspekty standardních testů. Práce jen zakončena vytvořením rámce pro filtrování dat pomocí námi navržených metod.
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Maximum likelihood estimators in time series
Tritová, Hana ; Pawlas, Zbyněk (advisor) ; Zikmundová, Markéta (referee)
The thesis deals with maximum likelihood estimators in time series. The reader becomes familiar with three important models for time series: autoregressive model (AR), moving average model (MA) and autoregressive moving average (ARMA). Thereafter he can find out the form of their main characteristics, e.g. population mean and variance. Then there is the derivation of parameter estimates - generally and for mentioned models of times series. There are also stated two other methods for finding estimators of AR(1) and MA(1) parameters - method of moments and least squares method. The end is dedicated to examples which compares all three methods.
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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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Value-at-risk forecasting with the ARMA-GARCH family of models during the recent financial crisis
Jánský, Ivo ; Rippel, Milan (advisor) ; Seidler, Jakub (referee)
The thesis evaluates several hundred one-day-ahead VaR forecasting models in the time period between the years 2004 and 2009 on data from six world stock indices - DJI, GSPC, IXIC, FTSE, GDAXI and N225. The models model mean using the AR and MA processes with up to two lags and variance with one of GARCH, EGARCH or TARCH processes with up to two lags. The models are estimated on the data from the in-sample period and their forecasting ac- curacy is evaluated on the out-of-sample data, which are more volatile. The main aim of the thesis is to test whether a model estimated on data with lower volatility can be used in periods with higher volatility. The evaluation is based on the conditional coverage test and is performed on each stock index sepa- rately. Unlike other works in this eld of study, the thesis does not assume the log-returns to be normally distributed and does not explicitly select a partic- ular conditional volatility process. Moreover, the thesis takes advantage of a less known conditional coverage framework for the measurement of forecasting accuracy.
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Evaluation of Methods for AR Coefficients Estimation Using Monte Carlo Analysis
Klejmova, Eva
Aim of this paper is to give recommendation for work with methods used for estimation of coefficients of autoregressive process. We applied Monte Carlo simulations to investigate performance of Burg, Yule-Walker and covariance methods. Evaluation of precision of spectral estimation is done with focus on signal length and lag order. The results are presented in graphical form and briefly discussed. Taking these results into account, Yule-Walker method shows better performance in case of long length signals and in case of overvalued lag order. Burg and covariance methods provide better results in case of short length signal and undervalued lag order.
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Analysis of wind speed distribution and applications in energy economics
Brož, Václav ; Červinka, Michal (advisor) ; Luňáčková, Petra (referee)
Analysis of wind speed distribution and applications in energy economics - an abstract Václav Brož 5 May 2015 Integration of generators of wind power into the electricity grid involves specific costs due to the intermittent nature of wind. Analysis of wind speed distribution is essential for accurate short-term prediction of wind power output in order to avoid mismatch between supply and demand in electricity markets. This thesis theoretically describes the analysis of wind speed distribution, high- lighting econometric and statistical concepts pertaining to the high persistence (modelling by the means of an AR(1) process) and the non-negativity (use of truncated normal distribution) of wind speed data. A random vector describ- ing the evolution of wind speed in time for a location in the Czech Republic is derived and its parameters are compared with those from the work of other authors. 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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