Random Fractal Time Series and the Teen-Birth Phenomenon

Abstract

The number of babies born to teenagers ranging in ages from 10 to 19 in the state of Texas during the years 1964 to 1990 is not strictly regular, but has both a systematic and random component. Herein we use the relative dispersion, the ratio of the standard deviation to the mean of a time series, to show by systematically aggregating the teen-birth data, that the correlation in the number of teen births is a modulated inverse power law. This scaling of the aggregated relative dispersion indicates the existence of long-time memory in the underlying control process and that the social process leading to teen pregnancy and having a baby are random, fractal and nonlinear. It is shown that this statistical behavior is the same as that observed in other sexual partner selection processes. We discuss the possible allometric nature of time series having such an inverse power-law character, and the implications of such memory for the properties of social control systems.