Variability Aware Recursive Neural Network (VARNN): A Residual-Memory Model for Capturing Temporal Deviation in Sequence Regression Modeling

Real-world time series data exhibit non-stationary behavior, regime shifts, and temporally varying noise (heteroscedastic) that degrade the robustness of standard regression models. We introduce the Variability-Aware Recursive Neural Network (VARNN), a novel residual-aware architecture for supervised time-series regression that learns an explicit error memory from recent prediction residuals and uses it to recalibrate subsequent predictions. VARNN augments a feed-forward predictor with a learned error-memory state that is updated from residuals over a short context steps as a signal of variability and drift, and then conditions the final prediction at the current time step. Across diverse dataset domains, appliance energy, healthcare, and environmental monitoring, experimental results demonstrate VARNN achieves superior performance and attains lower test MSE with minimal computational overhead over static, dynamic, and recurrent baselines. Our findings show that the VARNN model offers robust predictions under a drift and volatility environment, highlighting its potential as a promising framework for time-series learning.