Description

“Forecasting Limit Order Book Liquidity with Functional AutoRegressive Dynamics” (Chen, Chua & Härdle, 2016):

1️⃣ The limit order book (LOB) provides full snapshots of market liquidity through bid–ask volume curves.
2️⃣ Traditional scalar or vector autoregressions fail to capture the functional nature of these curves.
3️⃣ The paper introduces a Vector Functional AutoRegression (VFAR) model linking bid and ask liquidity dynamics.
4️⃣ Bid and ask functions are treated as elements in a Hilbert space ( H=L^2 ), connected via bounded linear operators.
5️⃣ Functional dependence is represented by kernel convolutions, estimated via B-spline sieves.
6️⃣ Consistency of the VFAR estimator is proven under entropy and sieve conditions.
7️⃣ Empirical analysis uses NASDAQ LOBSTER data (12 stocks, 44 trading days, 5-min intervals).
8️⃣ The VFAR yields R² above 95%, outperforming naïve forecasts in both RMSE and MAPE.
9️⃣ Multi-step forecasts (5–50 min ahead) show robust performance and smooth liquidity-curve prediction.
🔟 Conclusion: VFAR provides a functional framework for modeling cross-side liquidity and improving real-time market forecasting.