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 Verhulst 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.