  We present a stochastic model of population dynamics exploiting
cross-sectional data in trend analysis and forecasts for groups and cohorts of
a population. While sharing the convenient features of classic Markov models,
it alleviates the practical problems experienced in longitudinal studies. Based
on statistical and information-theoretical analysis, we adopt maximum
likelihood estimation to determine model parameters, facilitating the use of a
range of model selection methods. Their application to several synthetic and
empirical datasets shows that the proposed approach is robust, stable and
superior to a regression-based one. We extend the basic framework to simulate
ageing cohorts, processes with finite memory, distinguishing their short and
long-term trends, introduce regularisation to avoid the ecological fallacy, and
generalise it to mixtures of cross-sectional and (possibly incomplete)
longitudinal data. The presented model illustrations yield new and interesting
results, such as an implied common driving factor in obesity for all
generations of the English population and "yo-yo" dieting in the U.S. data.
