Analysis and forecasting of time series by averaged scalar products of flow vectors

Abstract

The relationship between the quality of state space reconstruction and the accuracy in time series forecasting is analyzed. The averaged scalar product of the dynamical system flowvectors has been used to give a degree of determinism to the selected state space reconstruction. This value helps distinguish between those regions of the state space here predictions will be accurate and those where they are not . A time series measured in an industri al environment where noise is present is used as an example. It is shown that prediction methods used to estimate futu re values play a less important role than a good reconstruction of the state space itself.Grateful acknowledgment is due to the ESPRIT project HI T E6447 for support of this work. One of us (R. H.) wants to thank to the M.E.C. for financial suppor