LAUSR

We develop a dynamic model to simultaneously characterize the liquidity demand and supply in a limit order book. The joint dynamics are modeled in a unified Vector Functional AutoRegressive (VFAR) framework. We derive a closed-form maximum likelihood estimator under sieves and establish asymptotic consistency of the proposed method under mild conditions. We find the VFAR model presents strong interpretability and accurate out-of-sample forecasts. In application to limit order book records of 12 stocks in the NASDAQ, traded from 2 January 2015 to 6 March 2015, the VFAR model yields values as high as 98.5% for in-sample estimation and 98.2% in out-of-sample forecast experiments. It produces accurate 5-, 25- and 50-min forecasts, with RMSE as low as 0.09–0.58 and MAPE as low as 0.3–4.5%. The predictive power stably reduces trading cost in the order splitting strategies and achieves excess gains of 31 basis points on average.