Liquidity fluctuations and the latent dynamics of price impact

Market liquidity is a latent and dynamic variable. We propose a dynamical linear price impact model at high frequency in which the price impact coefficient is a product of a daily, a diurnal, and an auto-regressive stochastic intraday component. We estimate the model using a Kalman filter on order book data for stocks traded on the NASDAQ in 2016. We show that our price changes estimates, conditional on order flow imbalance, on average (Formula presented.) of real price changes variance. Evidence is also provided on the fact that the conditioning on filtered information improves the estimate of the LOB liquidity with respect to the one obtained from a static estimation of the price impact. In addition, an out-of-sample analysis shows that our model provides a superior out-of-sample forecast of price impact with respect to historical estimates.