Description

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

1️⃣ The paper addresses forecasting of market liquidity via the entire limit order book (LOB) rather than single-point measures.
2️⃣ Bid and ask curves are treated as functional data, capturing the full shape of liquidity supply and demand.
3️⃣ Traditional VAR models ignore this continuous functional nature — motivating a Vector Functional AutoRegression (VFAR) approach.
4️⃣ The VFAR(1) model links past bid and ask functions through bounded linear operators estimated in Hilbert space.
5️⃣ Each operator is represented via B-spline kernel expansions and estimated using sieve maximum likelihoodmethods.
6️⃣ Theoretical results establish consistency of VFAR estimators under entropy and sieve regularity conditions.
7️⃣ NASDAQ LOBSTER data (12 stocks, 44 trading days, 5-min frequency) serve for empirical validation.
8️⃣ VFAR yields R² up to 98%, outperforming naïve benchmarks across RMSE and MAPE metrics.
9️⃣ The method captures cross-side (bid–ask) dependencies and provides accurate multi-step liquidity forecasts.
🔟 Conclusion: VFAR is a powerful, functional-data framework for real-time liquidity modeling and market microstructure prediction.