  We propose a new multivariate time series model in which we assume that each
component has a tendency to revert to the minimum of all components. Such a
specification is useful to describe phenomena where each member in a population
which is subjected to random noise mimics the behaviour of the best performing
member.
  We show that the proposed dynamics generate co-integrated processes.We
characterize the model's asymptotic properties for the case of two populations
and show a stabilizing effect on long term dynamics in simulation studies. An
empirical study involving human survival data in different countries provides
an example which confirms the occurrence of the phenomenon of reversion to the
minimum in real data.
