Abstract
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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URL
https://arxiv.org/abs/2609.06085
