With the fast growth of the international tourism industry, it has been a challenge to forecast the tourism demand in the international tourism market. Traditional forecasting methods usually suffer from the prediction accuracy problem due to the high volatility, irregular movements and non-stationarity of the tourist time series. In this study, a novel single dendritic neuron model (SDNM) is proposed to perform the tourism demand forecasting. First, we use a phase space reconstruction to analyze the characteristics of the tourism and reconstruct the time series into proper phase space points. Then, the maximum Lyapunov exponent is employed to identify the chaotic properties of time series which is used to determine the limit of prediction. Finally, we use SDNM to make a short-term prediction. Experimental results of the forecasting of the monthly foreign tourist arrivals to Japan indicate that the proposed SDNM is more efficient and accurate than other neural networks including the multi-layered perceptron, the neuro-fuzzy inference system, the Elman network, and the single multiplicative neuron model.

This paper presents a nonlinear model of human brain activity in response to visual stimuli according to Blood-Oxygen-Level-Dependent (BOLD) signals scanned by functional Magnetic Resonance Imaging (fMRI). A BOLD signal often contains a low frequency signal component (trend), which is usually removed by detrending because it is considered a part of noise. However, such detrending could destroy the dynamics of the BOLD signal and ignore an essential component in the response. This paper shows a model that, in the absence of detrending, can predict the BOLD signal with smaller errors than existing models. The presented model also has low Schwarz information criterion, which implies that it will be less likely to overfit the experimental data. Comparison between the various types of artificial trends suggests that the trends are not merely the result of noise in the BOLD signal.

A generalized radial basis function network consisting of (1 + cosh x)-1 as the basis function of the same class as Gaussian functions is investigated in terms of the feasibility of analog-hardware implementation. A simple way of hardware-implementing (1 + cosh x)-1 is proposed to generate the exact input-output response curve on an analog circuit constructed with bipolar transistors. To demonstrate that networks consisting of the basis function proposed actually work, the networks are applied to numerical experiments of forecasting chaotic time series contaminated with observational random noise. Stochastic gradient descent is used as learning rule. The networks are capable of learning and making short-term forecasts about the dynamic behavior of the time series with comparable performance to Gaussian radial basis function networks.

Time series prediction is very important technology in a wide variety of fields. The actual time series contains both linear and nonlinear properties. The amplitude of the time series to be predicted is usually continuous value. For these reasons, we combine nonlinear and linear predictors in a cascade form. The nonlinear prediction problem is reduced to a pattern classification. A set of the past samples x(n-1),. . . ,x(n-N) is transformed into the output, which is the prediction of the next coming sample x(n). So, we employ a multi-layer neural network with a sigmoidal hidden layer and a single linear output neuron for the nonlinear prediction. It is called a Nonlinear Sub-Predictor (NSP). The NSP is trained by the supervised learning algorithm using the sample x(n) as a target. However, it is rather difficult to generate the continuous amplitude and to predict linear property. So, we employ a linear predictor after the NSP. An FIR filter is used for this purpose, which is called a Linear Sub-Predictor (LSP). The LSP is trained by the supervised learning algorithm using also x(n) as a target. In order to estimate the minimum size of the proposed predictor, we analyze the nonlinearity of the time series of interest. The prediction is equal to mapping a set of past samples to the next coming sample. The multi-layer neural network is good for this kind of pattern mapping. Still, difficult mappings may exist when several sets of very similar patterns are mapped onto very different samples. The degree of difficulty of the mapping is closely related to the nonlinearity. The necessary number of the past samples used for prediction is determined by this nonlinearity. The difficult mapping requires a large number of the past samples. Computer simulations using the sunspot data and the artificially generated discrete amplitude data have demonstrated the efficiency of the proposed predictor and the nonlinearity analysis.

This paper proposes a prediction method for non-stationary time series data with time varying parameters. A modular structured type neural network is newly introduced for the purpose of grasping the changing property of time varying parameters. This modular structured neural network is constructed by the hierarchical combination of each neural network (NNT: Neural Network for Prediction of Time Series Data) and a neural network (NNW: Neural Network for Prediction of Weights). Next, we propose a reasonable method for determination of the length of the local stationary section by using the additive learning ability of neural networks. Finally, the validity and effectiveness of the proposed method are confirmed through simulation and actual experiments.