Mathematical analysis of stock market movement

One of the most popular today stochastic tool for estimating future movements of financial markets and forecasting daily returns, are GARCH-type processes. In order to use such a model in practice it is necessary to estimate its parameters. There are different ways to do it, but in applications the pseudo maximum likelihood (PSD) estimation is commonly used. Important advantage of this method is that it requires minimum of a priori information concerning probability distributions of innovation processes. The author analyzes the consistency and asymptotic normality properties of PSD estimator for GARCH processes.