Explainable Neural Networks for Price and Order-Flow Dynamics
Summary
The document uses a deep feed-forward network to study nonlinear interactions between high-frequency returns and signed trading volume in large- and small-tick stocks. It compares the network with a linear vector autoregression (VAR) and applies SHAP-based explanations to identify how recent lagged inputs contribute to predictions. The network improves predictive performance, particularly for returns, and the explanations emphasize the latest lags.
The analysis finds that lagged signed volume has sign-preserving effects that saturate, while lagged returns condition whether order flow continues, attenuates, or reverses price changes. Model-implied responses are checked against conditional averages reconstructed from data. The authors then use these patterns to build an interpretable nonlinear parametric model, including a multi-lag extension; it performs comparably to the neural network and better than the linear VAR. Findings are limited to the studied stocks and data setting, so they do not establish profitability or generalize automatically to other markets.
Key ideas
- A neural network can reveal nonlinear return and signed-volume dependencies that a linear VAR misses.
- SHAP explanations show that the most recent lags contribute most strongly to the forecasts.
- Lagged signed volume produces sign-preserving but saturating effects on returns.
- Lagged returns condition whether order-flow effects continue, weaken, or reverse.
- An interpretable nonlinear model can approximate the network's performance while retaining a multi-lag extension.
Tags
Full text
# Explainable Deep Learning for Price-Trade Dynamics: From Black-Box Forecasts to Effective Parametric Models # Explainable Deep Learning for Price-Trade Dynamics: From Black-Box Forecasts to Effective Parametric Models Understanding the joint dynamics of prices and trades is central to market microstructure, where returns and order flow interact through nonlinear and state-dependent mechanisms. Linear models are interpretable but may miss these effects, while deep neural networks improve forecasting at the cost of transparency. We use neural networks as tools for structural discovery rather than only for prediction. A deep feed-forward network is trained on high-frequency returns and signed volumes for large- and small-tick stocks and compared with a linear VAR benchmark. The neural network improves predictive performance, especially for returns, revealing nonlinear dependencies beyond the linear specification. Using Shapley-based explainability, we show that the dominant contributions are concentrated at the most recent lags. Model-implied responses are consistent with conditional averages reconstructed from the data. Unlike empirical averages, however, the neural-network decomposition isolates individual regressor contributions to the aggregate dependence. Lagged signed volume generates sign-preserving and saturating effects, consistent with nonlinear price impact and order-flow persistence. Lagged returns act as state variables: when the previous trade does not move the price, the model predicts continuation in the direction of past order flow, whereas non-zero returns generate attenuation or reversal. Building on these findings, we introduce a parsimonious SHAP-inspired nonlinear parametric model. It reproduces the main return-volume dependencies, outperforms the linear VAR benchmark, and achieves performance comparable to the neural network. A multi-lag extension captures residual longer-memory effects while preserving interpretability. Overall, explainability offers a route from black-box prediction to economically meaningful parametric models of price and trade dynamics.
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