The efficacy of the correlation dimension technique in detecting determinism in small samples

Abstract

This paper presents the results of a simulation study investigating the efficacy of the correlation dimension technique in detecting the presence of deterministic structure in small data sets. The results show that for some very simple structures a mere 100 data points suffice; but for some slightly more complicated structures, which arguably are still simple relative to real-world structures, even 2500 data points are inadequate. These results suggest that substantial caution be used in interpreting negative results on empirical data.

Keywords:

• Correlation Dimension
• Deterministic Structure
• Chaos

^∗We are grateful to Curt Taylor for his excellent and extensive programming assistance.

^∗We are grateful to Curt Taylor for his excellent and extensive programming assistance.

Notes

^∗We are grateful to Curt Taylor for his excellent and extensive programming assistance.