Complexity modelling and stability characterisation for long term iterated time series prediction

The authors describe a method of estimating and characterising appropriate data and model complexity in the context of long term iterated time series forecasting. In addition they also examine the stability of the neural network approach by extracting the dominant Lyapunov exponent from the neural network model itself. They extend the philosophy that the iterated prediction of a dynamical system can be interpreted through a model of the system dynamics. An embedding of a signal is obtained which decouples multiple time scale effects such as seasonality and trend. The performance of the technique is tested using a synthetic series, and real world time series problems including electricity load forecasting, and financial futures contracts.