Noise robust estimates of correlation dimension and K-2 entropy - art. no.016112

Using Gaussian kernels to define the correlation sum we derive simple formu las that correct the noise bias in estimates of the correlation dimension a nd K-2 entropy of chaotic time series. The corrections are only based on th e difference of correlation dimensions for adjacent embedding dimensions an d hence preserve the full functional dependencies on both the scale paramet er and embedding dimension. It is shown theoretically that the estimates, w hich are derived for additive white Gaussian noise, are also robust for mod erately colored noise. Simulations underline the usefulness of the proposed correction schemes. It is demonstrated that the method gives satisfactory results also for non-Gaussian and dynamical noise.