Residual Learning-Based Hybrid ARIMA–LSTM for Digital Retail Demand Forecasting

Abstract

The rapid growth of digital retail has increased the need for accurate demand forecasting to support inventory planning and operational decision-making. This study proposes and evaluates a residual learning-based Hybrid ARIMA–LSTM framework for daily retail demand forecasting. A univariate dataset containing 1,826 daily demand observations collected between January 2021 and December 2025 was preprocessed using data cleaning, Min–Max normalization, Augmented Dickey–Fuller (ADF) testing, first-order differencing, and sliding window transformation. ARIMA was employed to model the linear component of the demand series, while LSTM was used to learn nonlinear residual patterns. The proposed framework was evaluated against ARIMA, LSTM, Exponential Smoothing, Moving Average, and Naïve Forecast using MAE, MSE, and RMSE on the original demand scale after inverse normalization. The Hybrid ARIMA–LSTM achieved the lowest MSE (4668.71) and RMSE (68.32) among the evaluated forecasting models, whereas the standalone LSTM achieved a slightly lower MAE (49.87). Furthermore, residual analysis showed that the Hybrid ARIMA–LSTM produced stable forecasting performance, with residuals randomly distributed around the zero reference line, indicating minimal systematic prediction bias. This study demonstrates that a residual learning-based Hybrid ARIMA–LSTM framework can effectively improve daily digital retail demand forecasting by integrating statistical and deep learning models under identical experimental settings.