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Understanding the micro-dynamics of asset prices in modern electronic order books is crucial for investors and regulators. In this paper, we use an order-by-order Eurostoxx database spanning over 3 years to analyze the joint dynamics of prices and order flow. In order to alleviate various problems caused by high-frequency noise, we propose a double coarse-graining procedure that allows us to extract meaningful information at the minute time scale. We use Principal Component Analysis to construct �microstructure modes� that describe the most common flow/return patterns and allow one to separate them into bid-ask symmetric and bid-ask anti-symmetric. We define and calibrate a Vector Auto-Regressive (VAR) model that encodes the dynamical evolution of these modes. The parameters of the VAR model are found to be extremely stable in time, and lead to relatively high R² prediction scores, especially for symmetric liquidity modes. The VAR model becomes marginally unstable as more lags are included, reflecting the long-memory nature of flows and giving some further credence to the possibility of �endogenous liquidity crises�. Although very satisfactory on several counts, we show that our VAR framework does not account for the well-known square-root law of price impact.
Guillaume Maitrier (Sun,) studied this question.