The analysis and modelling of time series are in high demand because they can be encountered in real life situations. There are many everyday applications, such as weather forecast, prediction of currency exchange rates, etc. The goal is to predict the future values of time series from historical observations.
Several methods have been developed for the analysis and modelling of time series. Despite the numerous results it still remains an important research area because these results have left unanswered questions. One of these questions is for example, which method to use for which task as there is no definite technique to determine the appropriate, optimal method. Due to these questions the comparison of different time series modelling methods is still a current issue.
The aim of this thesis is to present certain linear and non-linear models of time series. The following linear models will be discussed, MA (moving average), AR (auto regressive), ARMA (auto regressive moving average) and finally ARIMA (auto regressive integral moving average). The dynamic neural network will be discussed as a possible implementation of the non-linear learning systems. The Echo State Network architecture will be discussed with detail which is a new implementation of the recurrent neural network.
By testing the different models I will compare them according to the following criteria: modelling ability, design questions and problems.