Nonparametric models of financial time series

In this diploma thesis we study basic models of time series, both parametric and nonparametric, and their basic properties. In the first part several conditional homoscedastic models are examined and the basic estimation methods are explained. Afterwards, we continue with conditional heteroscedastic models. We explain the reasons why are these models suitable to analyze financial time series. We state and prove the conditions for the strict stationarity of GARCH and calculate the mean square error (MSE) of prediction in GARCH(1,1). Eventually, the robustness of the least absolute deviation (LAD) method for GARCH is discussed and supported by numerical results. At the end of this thesis we discuss methods for nonparametric GARCH(1,1) estimation