Analysis and Forecasting of Time Series by Averaged Scalar Products of Flow Vectors
C. Santa Cruz
R. Huerta
Instituto de Ingenieri a del Conocimiento,
Universidad Autonoma de Madrid,
Canto Blanco, Mod. C-XVI, P.4, 28049 Madrid, Spain
J.R. Dorronsoro
Vicente López
Departamento de Ingenieri a Informatica,
Universidad Autonoma de Madrid,
Canto Blanco, 28049 Madrid, Spain
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 flow vectors 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 where predictions will be accurate and those where they are not. A time series measured in an industrial environment where noise is present is used as an example. It is shown that prediction methods used to estimate future values play a less important role than a good reconstruction of the state space itself.
