Differentiating between colored random noise and deterministic chaos with the root mean squared deviation

A method for distinguishing between data from a strange attractor and data from colored random noise is presented. For both types of data the apparent dimension, as measured by the scaling of the correlation function with len gth, is finite and noninteger for certain length scales. This would seem to indicate that such measurements by themselves are insufficient for conclud ing that the dynamics of the underlying system are low-dimensional. To dist inguish these two types of data, we have developed the variance growth test . The test looks for the increase in the variance, as measured by the avera ge squared deviation, of a subset of data as the length of that subset is i ncreased. For strange attractor data the variance saturates once the length of the subset exceeds the characteristic first return time. In contrast, t he variance of colored random noise continues to increase with increasing s ubset length indefinitely, with a scaling law that is related to the appare nt correlation dimension. Application of the method to the Bargatze data se t shows that the AL index behaves like a deterministic dynamical system.