Multiscale nonlinearity in a time series of weekly alcohol intake

Several authors have discussed the possibility that nonlinear dynamics might clarify substance abuse and chemical dependence. Nonlinear dynamical structure implies the possibility of oscillatory dynamics and high sensitivity to external perturbation. In this single-subject case study we analyzed the alcohol intake of a substance-abusing participant over a period of about five years using nonlinear time series analysis. The intake is measured in ounces per week and ounces per four weeks--approximately one month--yielding time series at two different time scales. We present statistical evidence that the participant's alcohol intake is nonlinear on both weekly and monthly time scales. We then discuss the implications of this multiscale nonlinearity for our understanding of substance abuse.