Multi-scale Representation of High Frequency Market Liquidity

We introduce an event based framework of directional changes and overshoots to map continuous financial data into the so-called Intrinsic Network - a state based discretisation of intrinsically dissected time series. Defining a method for state contraction of Intrinsic Network, we show that it has a consistent hierarchical structure that allows for multi-scale analysis of financial data. We define an information theoretic measurement termed Liquidity that characterises the unlikeliness of price trajectories and argue that the new metric has the ability to detect and predict stress in financial markets. We show empirical examples within the Foreign Exchange market where the new measure not only quantifies liquidity but also acts as an early warning signal.