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

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 it shows the VAR model presents a strong predictability in liquidity curves, with R 2 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.

A journey from univariate to multivariate functional time series: A comprehensive review

“…They extended hierarchical dynamic linear models for multivariate time series to the functional data setting, providing a powerful framework for analyzing complex and high-dimensional MFTS data. On the other hand, Chen, Chua, et al (2019) introduced a novel bivariate FTS model called the vector FAR (VFAR) model of order p. They conducted a comprehensive investigation of the model's estimation and asymptotic properties. Gao and Shang (2017) focused on analyzing mortality rates as a MFTS data.…”