Coding Economic Dynamics to Represent Regime Dynamics

In this paper a new approach to the analysis of the dynamics of economies is presented; applications to time series will also be suggested. In such applications, computational experiments may play a central role to provide a different heuristics and to explore data information. The approach is based upon ideas emerging in the literature on complex and chaotic dynamics, which imply that one can no longer rely on the fine description of classical dynamical systems: the state space structure breaks down, and instead of simple orbits, we should be satisfied with a description based upon symbolic trajectories, each symbol being associated with a partition of the original state space. Such partition can be induced by the introduction of the qualitative notion of regimes and of regime dynamics as a dynamics allowing for regime shifts. It can otherwise be suggested by preliminary data screening. Starting from a pre-set model, a regime is a set of dynamical paths generated by the same ?canonical model? with parameters. By identifying bifurcation values in the parameter space, one can classify a finite collection of realizations of such canonical model. A symbolic dynamical model reproduces dynamics across such sets of realisations, and can be tested against available empirical data. A preliminary exploration of some simple models yielding a finite (low-)number of regimes with a complex cross-regimes dynamics is presented, to motivate the move towards a discrete space dynamics and as a step towards the building of a general approach to multidimensional dynamical models