  We introduce a framework to study the effective objectives at different time
scales of financial market microstructure. The financial market can be regarded
as a complex adaptive system, where purposeful agents collectively and
simultaneously create and perceive their environment as they interact with it.
It has been suggested that multiple agent classes operate in this system, with
a non-trivial hierarchy of top-down and bottom-up causation classes with
different effective models governing each level. We conjecture that agent
classes may in fact operate at different time scales and thus act differently
in response to the same perceived market state. Given scale-specific temporal
state trajectories and action sequences estimated from aggregate market
behaviour, we use Inverse Reinforcement Learning to compute the effective
reward function for the aggregate agent class at each scale, allowing us to
assess the relative attractiveness of feature vectors across different scales.
Differences in reward functions for feature vectors may indicate different
objectives of market participants, which could assist in finding the scale
boundary for agent classes. This has implications for learning algorithms
operating in this domain.
