Forecasting limit order book liquidity supply–demand curves with functional autoregressive dynamics
提出了一个向量函数自回归模型，同时刻画限价订单簿中的流动性需求和供给，在纳斯达克12只股票数据上实现了高达98.5%的样本内拟合优度和98.2%的样本外预测精度，并能降低交易成本。
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 R2 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.