Abstract: Limit order book contains comprehensive information of liquidity on bid and ask sides. We propose a Vector Functional AutoRegressive (VFAR) model to describe the dynamics of the limit order book and demand curves and utilize the tted model to predict the joint evolution of the liquidity demand and supply curves. In the VFAR framework, we derive a closed-form maximum likelihood estimator under sieves and provide the asymptotic consistency of the estimator. In application to limit order book records of 12 stocks in NASDAQ traded from 2 Jan 2015 to 6 Mar 2015, it shows the VAR model presents a strong predictability in liquidity curves, with R2 values as high as 98.5 percent for insample estimation and 98.2 percent in out-of-sample forecast experiments. It produces accurate 5????; 25???? and 50????minute forecasts, with root mean squared error as low as 0.09 to 0.58 and mean absolute percentage error as low as 0.3 to 4.5 percent.

Key Words: Limit order book, Liquidity risk, multiple functional time series