Modelling Temporal Asymmetry in Industrial IoT Energy Data: A Comparative Study of Hybrid Statistical–Neural Forecasting Pipelines

Industrial energy consumption in shift-based manufacturing exhibits pronounced temporal asymmetry—here defined as direction-dependent conditional dynamics in which the transition from production to shutdown states follows a systematically different temporal trajectory than the reverse transition. At the facility studied, this asymmetry also manifests in the marginal distribution of hourly consumption values: pooling all 4724 observations yields a bimodal, right-skewed histogram (skewness ≈ −0.4) comprising two sub-populations corresponding to production hours (14–19 kWh/h) and shutdown hours (0–2 kWh/h). Although individual hourly observations are serially dependent and therefore not i.i.d., the marginal distributional shape is consequential because ARIMA-class models assume approximately Gaussian innovations, and residuals from models fit to this bimodal series inherit its non-Gaussianity. More fundamentally, the conditional distribution P(E_t|E_{t − 1}, …) is direction-dependent: the production-to-shutdown transition is abrupt (1–2 h, 18:00–20:00), while the shutdown-to-production ramp is slower and more variable (2–4 h, 05:00–07:00). Symmetric ARMA models, applying identical autoregressive coefficients regardless of transition direction, cannot represent this directional asymmetry, rendering their assumptions and associated error metrics structurally unreliable for this class of data. This paper addresses this asymmetry directly by presenting and evaluating two hybrid forecasting architectures—Prophet+LSTM and SARIMA+LSTM—for 24 h-ahead energy prediction at an industrial bread factory in Kazakhstan, instrumented with 15 IoT energy meters. The two-stage design exploits the complementary asymmetry-handling properties of each component: the statistical model (Prophet or SARIMA) captures deterministic seasonal structure, while the LSTM corrects asymmetric residuals that the statistical model systematically misrepresents. In a rigorous 14-day holdout evaluation, Prophet+LSTM achieves an MAE of 3.39 kWh—outperforming the Seasonal Naïve baseline by 12.3% and reducing Prophet-alone error by 32.7%—with statistical significance at the 10% level confirmed via Diebold–Mariano testing (DM = +1.747, p = 0.081). The LSTM residual correction reduces Prophet’s systematic negative bias by 69% (from −3.60 to −1.13 kWh), as confirmed by ablation testing. In eight weeks of production operation with incremental retraining, MAE improved 35% (7.02 → 4.58 kWh). These results demonstrate that explicitly modelling temporal asymmetry through hybrid statistical-neural architectures substantially improves industrial energy forecasting accuracy.