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A Negative Log Likelihood Function-Based Nonlinear Neural Network Approach

The most commonly used objective function in Artificial Neural Networks (ANNs) is the sum of squared errors. This requires the target and forecasted output vector to have the same dimension. In the context of nonlinear financial time series, both conditional mean and variance (volatility) tend to evolve over time. It is therefore of interest to consider neural networks with two-dimensional output even though the target data are one-dimensional. The idea of the back-propagation algorithm can be extended to this situation. For example, the negative log-likelihood based on a parametric statistical model is a possible alternative to the traditional least squares objective. It has been found that the RMSPE for the mean is smaller for of the developed neural network (LLNN) than traditional neural network (NN) in the majority cases. LLNN also provides comparable performance to NN for the real data set (Index of Stock Exchange of Thailand).