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Robust estimation of autocorrelation function
Lain, Michal ; Hudecová, Šárka (advisor)
The autocorrelation function is a basic tool for time series analysis. The clas- sical estimation is very sensitive to outliers and can lead to misleading results. This thesis deals with robust estimations of the autocorrelation function, which is more resistant to the outliers than the classical estimation. There are presen- ted following approaches: leaving out the outliers from the data, replacement the average with the median, data transformation, the estimation of another coeffici- ent, robust estimation of the partial autocorrelation function or linear regression. The thesis describes the applicability of the presented methods, their advantages and disadvantages and necessary assumptions. All the approaches are compared in simulation study and applied to real financial data. 1
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Robust estimation of autocorrelation function
Lain, Michal ; Hudecová, Šárka (advisor) ; Hlávka, Zdeněk (referee)
The autocorrelation function is a basic tool for time series analysis. The clas- sical estimation is very sensitive to outliers and can lead to misleading results. This thesis deals with robust estimations of the autocorrelation function, which is more resistant to the outliers than the classical estimation. There are presen- ted following approaches: leaving out the outliers from the data, replacement the average with the median, data transformation, the estimation of another coeffici- ent, robust estimation of the partial autocorrelation function or linear regression. The thesis describes the applicability of the presented methods, their advantages and disadvantages and necessary assumptions. All the approaches are compared in simulation study and applied to real financial data. 1
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Joinpoint Regression
Lain, Michal ; Maciak, Matúš (advisor) ; Hlávka, Zdeněk (referee)
The theme of this thesis is the joinpoint regression, the description of model, its properties and its construction. We are interested in methods of estimating parameters. We show practical use of the model. In the first chapter we define the model, we describe alternative forms and properties. In the second chapter we focus on estimating parameters of model. We briefly mention of Hudson method, profile likelihood, grid search and LASSO. We mention likelihood ratio for testing hypotheses about values of parameters. The third chapter deals with comparison of models by number of break points by permutation tests and information cri- terions. In the fourth chapter we deal with practical examples. We show diverse application of the model. We compare methods using simulations and show model application. 1
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