| Abstract: | It is well known that a nonlinear recursive equation can produce a chaotic sequence at certain values of the parameter. Furthermore, in the chaotic regime, extremely small changes in the initial value or in the value of the parameter produce very large changes in the sequence. It is surprising therefore that a short segment of a chaotic sequence can be used to reconstruct large portions of the sequence and to forecast future values of the sequence over short ranges. Furthermore, while the accuracy of the forecasts is dependent on the precision of the data, the relationship is much less sensitive than might have been expected. This is demonstrated by fitting a two-parameter model to two different types of chaotic equations: one a polynomial and the other a trigonometric function. This leads to the expectation that under certain circumstances, it may be possible to forecast values in a chaotic series over limited ranges, even if initial data are somewhat degraded. |
