Forecasting Limit Order Book Liquidity Supply-Demand Curves with Functional Autoregressive Dynamics

We develop a dynamic model to simultaneously characterize the liquidity demand and supply in limit order book. The joint dynamics is modelled 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 forecast. In application to limit order book records of 12 stocks in NASDAQ traded from 2 Jan 2015 to 6 Mar 2015, the VFAR model yields R2 values as high as 98.5 percent for in-sample estimation and 98.2 percent in out-of-sample forecast experiments. It produces accurate 5-, 25- and 50-$minute forecasts, with RMSE as low as 0.09 to 0.58 and MAPE as low as 0.3 to 4.5 percent. The predictive power stably reduces trading cost in the order splitting strategies and achieves excess gains of 31 basis points on average