| Research Abstract |
Now a day, we have a lot of problems, environmental disruption, environmental pollution, economic crisis, population problem, natural disaster, nature conservation, and so on. In order to solve these problems, it is very important to analyze progress of these phenomena. These phenomena can be regarded as time series. Mainly they are nonlinear time series. So, nonlinear prediction becomes very important.
(1) A Nonlinear Predictor
In this research project, we have developed a hybrid nonlinear predictor, which combines a neural network and a feed-forward linear predictor. Since the neural network has linear output unit, most of nonlinear part and some linear part can be predicted by the neural network. The remaining part is predicted by the linear predictor.
(2) Learning Algorithms
An improved learning algorithm has been proposed, which separately optimize the neural network and the linear predictor in this order. An enhanced learning algorithm has been proposed for noisy nonlinear time series prediction.
(3) Nonlinearity Analysis of Time Series
Prediction is the mapping from the past sample x(n-1)=[x(n-1),x(n-2),..,x(n-N)] to the next sample x(n). When the past samples x(nィイD21ィエD2-1) and x(nィイD22ィエD2-1) are similar, however, the next samples x(nィイD21ィエD2) and x(nィイD22ィエD2) are far from to each other, then, nonlinearity of this time series is high. A measure, which can evaluate this property has been introduced.
(4) Prediction of Real Nonlinear Time Series
The proposed method was applied to many the real nonlinear time series, including Chaos, water levels of some lake, fog generation, and so on. The proposed hybrid nonlinear predictor demonstrated good performance compared with the conventional methods.
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