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This paper deals with higher order feed-forward neural networks with a new activation function - neuron-adaptive activation function. Experiments with function approximation and stock market movement simulation have been conducted to justify the new activation function. Experimental results have revealed that higher order feed-forward neural networks with the new neuron-adaptive activation function present several advantages over traditional neuron-fixed higher order feed-forward networks such as much reduced network size, faster learning, and more accurate financial data simulation.