ESTIMATING DIMENSIONS WITH CONFIDENCE

Estimation of correlation and other fractal dimensions is a favored approach for investigating whether time series or other dynamical data may be produced by nonlinear deterministic systems. The standard methods have disadvantages which are widely recognised; briefly put, an estimate is always produced, with no indication of its reliability or likely error. By assuming an explicit geometrical model for an attractor, we are able to produce a better estimator and to give a form of weak confidence intervals. Experience so far indicates that this approach is much less likely to give misleading answers than the conventional ones.