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Backtesting of Time Series Models
Stroukalová, Marika ; Houfková, Lucia (advisor) ; Zichová, Jitka (referee)
Title: Backtesting of Time Series Models Author: Marika Stroukalová Department: Department of Probability and Mathematical Statistics Supervisor: Mgr. Lucia Jarešová Supervisor's e-mail address: lucia.jaresova@centrum.cz Abstract: In the present work we study the basic models of financial time series (ARMA, GARCH), we focus on parameter estimation and forecasting in estimated models. We describe the means of estimating parametres and future values in the program R. In the theoretical section we also discuss the features of financial time series, define simple returns and log returns and we introduce the benefits of the log returns. We also apply the white noise model, ARMA(1,1) and GARCH(1,1) on historic time series of logarithmic returns of chosen stock exchange indices, we also backtest 1-step ahead fore- cats and 5-step ahead forecasts and we compare the results of these models. By empirical comparison of real data we also analyze how the models reac- ted on the present financial crisis and evaluate how the normal distribution assumption for the data held up. Keywords: time series, ARMA, GARCH, backtesting. 1
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Modelling Bonus - Malus Systems
Stroukalová, Marika ; Mazurová, Lucie (advisor) ; Prokešová, Michaela (referee)
Title: Modelling Bonus - Malus Systems Author: Marika Stroukalová Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Lucie Mazurová, Ph.D., KPMS MFF UK Abstract: In this thesis we deal with bonus-malus tariff systems commonly used to adjust the a priori set premiums according to the individual claims during mo- tor third party liability insurance. The main aim of this thesis is to describe the standard model based on the Markov chain. For each bonus-malus class we also determine the relative premium ("relativity"). Another objective of this thesis is to find optimal values for the relativities taking into account the a priori set premiums. We apply the theoretical model based on the stationary distribu- tion of bonus-malus classes on real-world data and a particular real bonus-malus system used in the Czech Republic. The empirical part of this thesis compares the optimal and the real relativities and assesses the suitability of the chosen theoretical model for the particular bonus-malus system. Keywords: bonus-malus system, a priori segmentation, stationary distribution, relativity, quadratic loss function 1
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Modelling Bonus - Malus Systems
Stroukalová, Marika ; Mazurová, Lucie (advisor) ; Prokešová, Michaela (referee)
Title: Modelling Bonus - Malus Systems Author: Marika Stroukalová Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Lucie Mazurová, Ph.D., KPMS MFF UK Abstract: In this thesis we deal with bonus-malus tariff systems commonly used to adjust the a priori set premiums according to the individual claims during mo- tor third party liability insurance. The main aim of this thesis is to describe the standard model based on the Markov chain. For each bonus-malus class we also determine the relative premium ("relativity"). Another objective of this thesis is to find optimal values for the relativities taking into account the a priori set premiums. We apply the theoretical model based on the stationary distribu- tion of bonus-malus classes on real-world data and a particular real bonus-malus system used in the Czech Republic. The empirical part of this thesis compares the optimal and the real relativities and assesses the suitability of the chosen theoretical model for the particular bonus-malus system. Keywords: bonus-malus system, a priori segmentation, stationary distribution, relativity, quadratic loss function 1
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Backtesting of Time Series Models
Stroukalová, Marika ; Houfková, Lucia (advisor) ; Zichová, Jitka (referee)
Title: Backtesting of Time Series Models Author: Marika Stroukalová Department: Department of Probability and Mathematical Statistics Supervisor: Mgr. Lucia Jarešová Supervisor's e-mail address: lucia.jaresova@centrum.cz Abstract: In the present work we study the basic models of financial time series (ARMA, GARCH), we focus on parameter estimation and forecasting in estimated models. We describe the means of estimating parametres and future values in the program R. In the theoretical section we also discuss the features of financial time series, define simple returns and log returns and we introduce the benefits of the log returns. We also apply the white noise model, ARMA(1,1) and GARCH(1,1) on historic time series of logarithmic returns of chosen stock exchange indices, we also backtest 1-step ahead fore- cats and 5-step ahead forecasts and we compare the results of these models. By empirical comparison of real data we also analyze how the models reac- ted on the present financial crisis and evaluate how the normal distribution assumption for the data held up. Keywords: time series, ARMA, GARCH, backtesting. 1
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