Nonlinear prediction of noisy time series with feedforward networks

The main focus of this study is the investigation of the noise filtering capabilities of the feedforward networks with small data sets. The first stage focuses on deterministic nonlinear time series estimation. The quality of the results with deterministic data will serve as a benchmark performance of the estimation techniques under study. The second stage involves the investigation of the out-of-sample performance of feedforward networks with noisy data sets. The noise component is investigated as a measurement noise. Basically, the in-sample and the out-of-sample mean square errors, sign predictions and the estimates of the Lyapunov exponents are used as the criteria of the fit and the quality of the forecasts. Although there has been some work done with feedforward networks within the context of nonlinear function approximation, the out-of-sample forecast capabilities of these are not yet investigated. This issue is addressed within the framework of the inverse problem. As compared to the other commonly used approximation techniques, the results of this study show that feedforward networks may prove to be an invaluable technique in the prediction of noisy time series data.

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