Multi-scale representation of high frequency market liquidity

We introduce an event based framework mapping financial data onto a state based discretisation of time series. The mapping is intrinsically multi-scale and naturally accommodates itself with tick-by-tick data. Within this framework, we define an information theoretic quantity that characterises the unlikeliness of price trajectories and, akin to a liquidity measure, detects and predicts stress in financial markets. In particular, we show empirical examples within the foreign exchange market where the new measure not only quantifies liquidity but also seems to act as an early warning signal.