| 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 fitted 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䀀; 25䀀 and 50䀀-inute 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. |