ABSM: A Trajectory-Stable Post-Prediction Stabilization Framework for Financial Time-Series Forecasting under Noisy Market Dynamics

This work proposes a post-prediction stabilization framework for financial time-series forecasting using the Adaptive Balancing Scaling Model (ABSM). The framework integrates classical statistical models and deep learning architectures including ARIMA, LSTM, GRU, and XGBoost with a nonlinear trajectory stabilization layer designed to reduce forecast volatility under noisy market dynamics. Unlike conventional approaches focused solely on prediction error minimization, this study investigates trajectory stability, variance contraction, and directional consistency in financial forecasting systems. ABSM operates as a model-agnostic post-processing transformation that attenuates high-deviation predictions without modifying the underlying forecasting architecture. Experiments conducted on NSE stock datasets demonstrate improved trajectory smoothness and reduced variance propagation, particularly for nonlinear recurrent models. The work connects financial forecasting with concepts from stochastic contraction theory and dynamical systems stabilization. Keywords: Financial Forecasting, ABSM, Time-Series Analysis, LSTM, GRU, ARIMA, XGBoost, Stochastic Stability, Forecast Stabilization, Trajectory Contraction.