This paper introduces an adaptive Higher Order Neural Network (HONN) model and applies it in data mining such as simulating and forecasting government taxation revenues. The proposed adaptive HONN model offers significant advantages over conventional Artificial Neural Network (ANN) models such as much reduced network size, faster training, as well as much improved simulation and forecasting errors. The generalization ability of this HONN model is explored and discussed. A new approach for determining the best number of hidden neurons is also proposed.