Extending Deep Learning Models for Limit Order Books to Quantile Regression
Extending Deep Learning Models for Limit Order Books to Quantile Regression
This paper extends deep learning models for limit order books (LOBs) to quantile regression, proposing a novel architecture called DeepLOB-QR. The model simultaneously predicts multiple quantiles (0.25, 0.5, 0.75) of future returns for both long and short positions, using a shared convolutional block for feature extraction from raw LOB data and separate LSTM branches for each quantile. A key contribution is the definition of returns that explicitly account for bid-ask spreads, making the predictions more realistic for intraday trading. The authors also introduce a forecast combination method that linearly combines quantile estimates via constrained least squares to produce a robust point prediction.
Experiments are conducted on a large dataset of over 134 million LOB updates from five liquid stocks on the London Stock Exchange. DeepLOB-QR outperforms traditional models (AR, GLR, SVR, MLP) in terms of MAE, MSE, MeAE, and R² for both long and short positions. The forecast combination further improves performance, demonstrating the value of using multiple quantiles. The results highlight the effectiveness of deep learning and quantile regression in capturing the complex, non-stationary dynamics of high-frequency financial data, providing both accurate point forecasts and uncertainty estimates.
Highlights
- 1Proposes DeepLOB-QR, a deep learning architecture that simultaneously models multiple return quantiles for both long and short positions using limit order book data.
- 2Introduces a novel return definition that accounts for bid-ask spreads, improving realism for intraday trading strategies.
- 3Demonstrates that combining quantile estimates via constrained regression yields better point predictions than using the median alone.
- 4Validates the model on a large-scale dataset of over 134 million LOB updates from the London Stock Exchange, outperforming AR, GLR, SVR, and MLP baselines.
Methods
- MQuantile Regression (QR) with multiple quantile loss functions to estimate conditional quantiles of returns.
- MConvolutional neural network (CNN) for feature extraction from raw limit order book data.
- MMulti-branch LSTM layers to capture temporal dependencies and model different quantiles simultaneously.
- MForecast combination via constrained least squares to aggregate quantile estimates into a point prediction.
Results
- RDeepLOB-QR achieves lower MAE, MSE, MeAE, and higher R² compared to AR, GLR, SVR, and MLP for both long and short position returns.
- RCombining quantile estimates (DeepLOB-QR(C)) further improves prediction accuracy over using the median alone.
- RPerformance degrades as prediction horizon increases (k=50, 100, 200), but DeepLOB-QR remains competitive.
- RThe model effectively captures asymmetric returns from long and short positions due to varying spreads.
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