Noise reduction methods and the Grassberger-Procaccia algorithm. A simulation study

The behaviour of the Grassberger-Procaccia algorithm is analysed when applied to noisy data and the possibility of improving its performance by pre-filtering the series with some of the noise reduction methods proposed in the literature. The results, obtained from series simulated from well known chaotic systems with different levels of noise added, allow us to conclude: (1) that the distortion caused by noise is unequal, and (2) that the best result is obtained when the series are pre-processed by means of the 'singular value decomposition' method.