Structure and properties of GARCH(1,1) model

The aim of this thesis is to introduce the reader an econometric approach to financial time series volatility modeling and scrutinize construction, properties and constraints of the popular GARCH(1,1) model when applying it on real market data and in wider sense than it's usually presented in reference literature. In the section 1 we'll repeat some important statistical terms of time series econometrics, which will be needed in next sections. We'll talk a little bit more generally about volatility of an asset, its modeling and measuring at all, because the true values are actually unknown and we observe just its demonstration on the markets. We'll mention some important statistical tools operating as an irreplaceable component of the GARCH(1,1) model, which will be introduce in the section 2. We'll scrutinize its specific properties, advantages, constraints and indeed the statistical inference. Because it's considered as a flexible model with rather general structure we'll also discuss some complications which can occur during its applications and convenient ways to solve them. Implementation of the model will be presented in the section 3. We'll use real market data and show clear demonstration of the scrutinized properties. At the end we'll verify how the model is significant when explaining the volatility of an asset.