The analysis and prediction of stock market processes are extremely important economic tasks. Better economic decisions can be made with the help of more precise predictions, which leads to a better allocation of the resources that helps progress. The complexity and difficulty of this problem is proved by that there is no complete agreement on how much time series analysis could contribute to the improvement of the prediction. Some researchers believe that all the information is already “coded” in the price therefore no investor can “beat the market” by analyzing historical data – this is called the Efficient Market Hypothesis. Contrarily most analysts believe that there are recurring patterns in the market which can be identified and predicted (the market does not always show the fair, true value of the price).
Stock market (or in general: financial) time series examined for a longer period show several hardly manageable, problematic characteristics. Besides that there are only a small amount of samples and the time series itself is non-stationary, non-linear and contains high noise the following facts make the prediction even harder:
• Outliers can occur in a period which is otherwise considered to be event-free.
• From time to time the behavior of the time series changes (for example it changes from a stagnant or growing period to a decreasing one).
In my thesis I apply an approach which has been less examined in the literature. This approach is based on the detection of outliers and change points and on the adaptation of the prediction using this information - since the outliers and change points can deceive the prediction system. In my thesis I introduce time series in general, furthermore I review the most frequently used models (such as ARIMA) concerning the analysis of time series. I present the literature about detecting outliers and change points and also about the prediction of time series. I apply several methods in these areas and I also test these methods on simulated and on real data. Finally I describe this combined prediction system which uses the detection of outliers and change points for the forecasting. I test the prediction system and also compare its results to previous works.