Hybrid SARIMA LSTM Model for Local Weather Forecasting: A Residual Learning Approach for Data Driven Meteorological Prediction

Accurately forecasting long-term atmospheric variables remains a defining challenge in meteorological science due to the chaotic nature of atmospheric systems. Temperature data represents a complex superposition of deterministic cyclical climate forces and stochastic, short-term fluctuations. While planetary mechanics drive predictable seasonal periodicities, rapid meteorological changes such as thermal variations, pressure anomalies, and humidity shifts introduce nonlinear volatilities that defy simple extrapolation. Historically, the Seasonal Autoregressive Integrated Moving Average (SARIMA) model has been the standard for modeling historical weather data, prized for capturing linear seasonal trends. However, SARIMA operates under strict assumptions of stationarity, failing to capture abrupt, nonlinear transitions. This leads to systematic residual errors, manifesting as the under-prediction of sudden spikes or the over-smoothing of declines. Conversely, Deep Learning paradigms, specifically Long Short-Term Memory (LSTM) networks, demonstrate exceptional efficacy in handling intricate time-series data. By utilizing memory gates, LSTMs learn complex nonlinear dependencies. Yet, LSTMs face instability in open-loop forecasting; without ground truth feedback, minor deviations compound recursively, causing divergence. To resolve these limitations, we propose a Hybrid SARIMA-LSTM architecture. This framework employs a residual-learning strategy to decompose temperature into a predictable climate component and a nonlinear weather component. The SARIMA unit models the robust, long-term seasonal trend, while the LSTM is trained exclusively on the residuals the nonlinear errors SARIMA fails to capture. By fusing statistical stability with neural plasticity, this hybrid approach minimizes error propagation and enhances long-horizon accuracy.