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Linear regression model with autocorrelated residuals
Kostka, Ján ; Zichová, Jitka (advisor) ; Hudecová, Šárka (referee)
The aim of this bachelor thesis is to introduce the algorithm for analysis of the linear regression model with autocorrelated residuals, which is applicable to time series data. For residuals, we assume the ARMA model, eventually ARIMA model, which enlarges the possibilities of application. The analysis of such regression models includes detection of autocorrelation and related tests, detection of stationarity and related unit root test, followed by model identification for residuals and maximum likelihood estimation of identified regression model.
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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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Natural rate of unemployment or hysteresis? The case of the Czech Republic
Bechný, Jakub ; Potužák, Pavel (advisor) ; Kadeřábková, Božena (referee)
The aim of this thesis is to empirically investigate, using stationarity and unit root tests, whether is the labor market of the Czech Republic developing accordingly to the natural rate of unemployment theory, or the hysteresis theory. Taking into consideration a structural break in the second half of the nineties I conclude, that the hysteresis at the national level works only in unemployment. Employment data, on the other hand, do not indicate the hysteresis. Unemployment tests on the regional level then suggest, that transitory shocks have permanent effects only in half of the regions.
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