Grey system theory-based models in time series prediction

Being able to forecast time series accurately has been quite a popular subject for researchers both in the past and at present. However, the lack of ability of conventional analysis methods to forecast time series that are not smooth leads the scientists and researchers to resort to various forecasting models that have different mathematical backgrounds, such as artificial neural networks, fuzzy predictors, evolutionary and genetic algorithms. In this paper, the accuracies of different grey models such as GM(1,1), Grey Ver-hulst model, modified grey models using Fourier Series is investigated. Highly noisy data, the United States dollar to Euro parity between the dates 01.01.2005 and 30.12.2007, are used to compare the performances of the different models. The simulation results show that modified grey models have higher performances not only on model fitting but also on forecasting. Among these grey models, the modified GM(1,1) using Fourier series in time is the best in model fitting and forecasting. A time series is a collection of data points which are generally sampled equally in time intervals. Time series prediction refers to the process by which the future values of a system is forecasted based on the information obtained from the past and current data points. Generally, a pre-defined mathematical model is used to make accurate predictions. Time series prediction models are widely used in financial area, such as predicting stock price indexes , foreign currency exchange rates (FX rates) and so on. The ability to do prediction with a reasonable accuracy can change the economic policy of large companies and governments and ensure a more reasonable behavior by the financial actors. Statistical and artificial intelligence (soft computing) based approaches are the two main techniques for time series prediction seen in the literature. are widely used as an artificial intelligence based approach, back propagation being the most widely used technique for updating the parameters of the model. However , not only are the statistical models not as accurate as the neu-ral network-based approaches for nonlinear problems, they may be too complex to be used in predicting future values of a time series. One major criticism about the NN model is that it demands a great deal of training data and relatively long training period for robust generalization (Jo, 2003). Other intelligent approaches seen in the literature for the analysis of time series include Linear regression, a combination of genetic algorithms and neural networks has been …