The main purpose of this paper is to propose a neuron model based on dendritic mechanisms and a phase space reconstruction (PSR) to analyze XAUUSD (Gold/U.S. Dollar), EURUSD (Euro Fx/U.S. Dollar), GBPJPY (British Pound/Japanese Yen), and USDJPY (U.S. Dollar/Japanese Yen). We reconstruct the time series of exchange rate by using the PSR to prove that attractors exist for the systems constructed. In this way, it is able for us to observe the attractors obtained intuitively in a three-dimensional search space, which make it easier to analyze the characteristics of dynamic systems. In the forecasting procedure, we employ the maximum Lyapunov exponent to identify the chaotic properties and the reciprocal to determine the limit of prediction, by using the reconstructed phase space. Short-term predictions are also made based on the dendritic neuron model after the experiment, which resulted that the proposed methodology performed better than the traditional multi-layered perceptron and the Elman neural network in the light of prediction accuracy and training time.
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