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Nonlinearity detection in financial time series
 Dudlák, Oliver ; Zichová, Jitka (advisor) ; Prášková, Zuzana (referee)
The aim of this master thesis is nonparametric and parametric nonlinearity testing in time series and its application on real financial data. From nonparametric tests, we describe a bispectral density test. Based on it, we can test symmetry and linearity of observed time series. Because of complex nature of the test we included the theory of complex random variable. From parametric tests, we introduce the RESET test and its modifications, Keenan test and F test. Considering the analogy between these tests and the test for submodel in linear model, we included basic theory of linear model and multivariate linear regression model. For both cases we performed a simulation study, where we observe frequencies of rejections of null hypothesis in both linear and nonlinear time series. When we get frequencies corresponding to the theoretical significance levels of the test, statistics we continue analyzing the real data.
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Nonparametric Nonlinearity Testing in Time Series
 Dudlák, Oliver ; Zichová, Jitka (advisor) ; Prášková, Zuzana (referee)
The aim of this bachelor thesis is nonparametric nonlinearity time series testing by using Q-tests and BDS-test. We describe theoretically each of the tests and then use them on simulated and real historical data. For tested time series we firstly try to identify linear model ARMA(p,q). Then we apply the tests on the estimated white noise to test the assumption of independence or noncorrelation and verify the accuracy of identified model.
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