Hanaihau Hargous

Deterministic cycles and random excursions

by John Reid

Random walks are the outcome of a summing or integrating process and as such are widespread in nature. They are manifested as power law relationships between variance density and frequency. The random walk effect may be removed by differencing and decimating the data. In this way it is possible to show that apparently deterministic cycles observed in some natural time series are, in fact, random walk excursions.