Abstract: Traditional forcasting method is to establish subjective model of data series firstly, then calculate and forecast according to subjective model. With the development of chaotic science, it doesn't have to establish subjective model beforehand, but forecasts directly and subjectivity of forecasting can be avoided by objective laws(as Lyapunov exponent etc.) calculated by data series themselves. The method put forward by this paper applies small data series, almost utilizes all available data information, and can calculate accurate lyapunov exponent. Results show that the method is credible with small calculation amount, easy operation relatively, high precision, and is able to get maximal forecasting time.

Key words: largest lyapunov exponent, small data sets, chaotic time series, forecasting