Neural network chaos and computational algorithms of forecast in finance

Dynamic system chaos theory has given us a new view of the world. Systems that are apt to chaotic behavior must possess the main properties: non-linearity, openness as a system, multicomponentness, evolutionism and randomness. In such systems, even a slight change in initial conditions could cause it to evolve into a new macroscopic structure or, in other words, a cooperative mode discovered under fluctuations. The significance of asymmetry and non-linearity, which were increased on introducing a restricted N-shaped synaptic relation in a two-mode dynamic model, is emphasized. Population dynamics, economics, weather and financial market forecasting possess these properties. Long-term forecasting of chaotic systems is almost impossible because a small error can amplify itself over time to cause a new quality of events. Short-term forecasting of chaotic systems can easily realized, moreover chaos is a catalyst in the learning of artificial neural systems. An improved neural network computational algorithm linked with the kernel function approach and the recursive prediction error method has been developed and applied to stock market time series forecasting. The main idea of neural network learning by the kernel function is that this function stimulates changes to weights to achieve convergence of desired and forecast output functions.