Weak Relation Enforcement for Kinematic-Informed Long-Term Stock Prediction with Artificial Neural Networks
Stanislav Selitskiy
TL;DR
The paper tackles spurious, non-physical predictions in long-term stock forecasting by enforcing velocity relations using a KINN framework that combines graph-based relations with physics-informed constraints. It introduces a two-term loss $L = L_v + L_{ve}$ that penalizes prediction errors and enforces $v_t \approx v_{t-1} + e_{t-1}$, with a GNN mapping past indices and velocities to future values and velocities. Extensive experiments across multiple architectures and stocks (Dow Jones, NASDAQ, NIKKEI, DAX) demonstrate statistically significant improvements for normalization-sensitive models and reduced spurious behavior, highlighting the importance of velocity-consistent dynamics in non-stationary time series. The work also discusses normalization-related limitations and outlines future directions, including extending to multi-parameter inputs/outputs and incorporating attention and sparse training to adapt to temporal changes without forgetting past information.
Abstract
We propose loss function week enforcement of the velocity relations between time-series points in the Kinematic-Informed artificial Neural Networks (KINN) for long-term stock prediction. Problems of the series volatility, Out-of-Distribution (OOD) test data, and outliers in training data are addressed by (Artificial Neural Networks) ANN's learning not only future points prediction but also by learning velocity relations between the points, such a way as avoiding unrealistic spurious predictions. The presented loss function penalizes not only errors between predictions and supervised label data, but also errors between the next point prediction and the previous point plus velocity prediction. The loss function is tested on the multiple popular and exotic AR ANN architectures, and around fifteen years of Dow Jones function demonstrated statistically meaningful improvement across the normalization-sensitive activation functions prone to spurious behaviour in the OOD data conditions. Results show that such architecture addresses the issue of the normalization in the auto-regressive models that break the data topology by weakly enforcing the data neighbourhood proximity (relation) preservation during the ANN transformation.