Detecting chaos in a noisy time series.

We propose a new method for detecting low-dimensional chaotic time series when there is dynamical noise present. The method identifies the sign of the largest Liapunov exponent and thus the presence or absence of chaos. It also shows when it is possible to assign a value to the exponent. This approach can work for short time series of only 500 points. We analyse several real time series including chickenpox and measles data from New York City. For model systems it correctly identifies important spatial scales at which noise and nonlinear effects are important. We propose a further technique for estimating the level of noise in real time series if it is difficult to detect by the former method.