LEARNING THE RULE OF A TIME SERIES
Idit Ginzberg, D. Horn · International Journal of Neural Systems · 1992
Neural networks can be trained to predict the next value of a time series on the basis of its preceding values. We try to find out how well such a network approximates the rule which underlies the series. For this purpose, we study the net-sequence, which is a long time series generated iteratively by the network. We introduce a new measure: the difference between the distributions of function values in the data and the net-sequence. We demonstrate its usefulness on the problem of the chaotic quadratic map. Adding random noise to the series we find, by using this tool, that the networks can approximate well the correct rule only if the noise amplitude is very small. Applying the new measure as a weak constraint in the problem of sunspot data, we see that it correlates well with the ability of the network to predict several time steps into the future.