Stochastic difference equations of the Box-Jenkins form provide an adequate family of models on which to base the stochastic theory of human growth processes, but conventional time series identification methods do not apply to available data sets. A method to identify structure and parameters of stochastic difference equation models of human growth is presented. The practicality of the method is demonstrated in two applications to human growth data. The data sets are: (1) IQ data for 80 subjects over a period of 14 years, from the Fels Institute Longitudinal Sample. (2) Preschool readiness test data for 110 subjects over a period of two years, from the National Day Care Center (NDCS) Longitudinal Sample. Applicability of stochastic system theory to cognitive growth problems is established. In the Fels data, the existence of a stochastic component to growth is demonstrated. The findings support the psychological hypothesis that IQ is, not as much a stable human trait as it is a dynamic phenomenon that exhibits real, persistent changes in response to changing environments. An upper bound to "heritability" of IQ in the Fels population was computed; it is substantially lower than other figures quoted in the literature. (Author/RD)