Forecasting limit order book liquidity supply–demand curves with functional autoregressive dynamics

Abstract

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 $R^2$ 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.

Keywords:

• Liquidity demand and supply curves
• Order splitting strategy
• Vector functional autoregression
• Liquidity forecasting
• Time series

JEL Classification:

• C13
• C32
• C53

Acknowledgments

We would like to thank the editor and two anonymous referees for their constructive comments to help improve the quality of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The research of Ying Chen is supported by the Academic Research Funding R-155-000-178-114 and IDS Funding R-155-000-185-64 at the National University of Singapore. Support from IRTG 1792 ‘High Dimensional Non Stationary Time Series’, Humboldt-Universität zu Berlin, is gratefully acknowledged.