📈 Retail Sales Forecasting with ARIMA and LSTM
Model Details
This project compares two forecasting approaches for retail sales prediction:
- ARIMA (AutoRegressive Integrated Moving Average)
- LSTM (Long Short-Term Memory neural network)
The models were trained and evaluated using a rolling window evaluation across 40 windows. Both models were assessed using RMSE, MAE, and stability metrics.
Frameworks used:
- ARIMA:
statsmodels,pmdarima - LSTM:
TensorFlow / Keras
Evaluation Summary
| Model | Avg RMSE | Std RMSE | Avg MAE | Std MAE | Min RMSE | Max RMSE |
|---|---|---|---|---|---|---|
| ARIMA | 3,175,011.32 | 763,036.27 | 2,448,829.54 | 950,375.79 | 2,195,796.46 | 6,171,402.14 |
| LSTM | 3,169,389.04 | 729,371.84 | 2,435,767.99 | 912,025.28 | 2,252,916.59 | 6,016,384.05 |
🏆 Winner: LSTM – better generalization and stability.
Short Report: Model Generalization Discussion
Both ARIMA and LSTM models were evaluated using a rolling window approach over 40 windows. The results indicate that LSTM slightly outperforms ARIMA, with an average RMSE of 3,169,389 compared to ARIMA’s 3,175,011. While the absolute difference is small (≈0.2%), the consistency of LSTM predictions is notable, as reflected in its lower RMSE standard deviation (729,371 vs. 763,036).
The reason LSTM generalizes better is that it can capture complex nonlinear temporal dependencies in the sales data, which ARIMA (a linear statistical model) cannot fully represent. This advantage is especially relevant for retail sales, where seasonality, promotions, and external factors often introduce nonlinear fluctuations.
In terms of stability, LSTM’s tighter error range suggests that it adapts more consistently across different rolling windows, further supporting its robustness. While ARIMA remains a strong baseline for time series forecasting, LSTM demonstrates better generalization capability due to its ability to learn hidden patterns that extend beyond simple trend and seasonality.
Conclusion:
The LSTM model generalizes better than ARIMA for this dataset because it handles complex patterns and provides more stable performance, making it the preferred choice for future forecasting.
Intended Use
- Task: Time Series Forecasting (Daily Retail Sales Prediction)
- Domain: Retail / E-commerce demand forecasting
- Forecast Horizon: 30 days
This model can be applied to predict daily sales, assist in inventory management, staff scheduling, and strategic planning.
Training Procedure
- Dataset: Rossmann-like retail sales dataset (merged
train.csv+store.csv) - Preprocessing:
- Removed closed days and zero-sales days
- Aggregated to daily level
- Scaled features for LSTM
- Models:
- ARIMA (
pmdarima.auto_arima) - LSTM with 3 stacked layers (25 units each, dropout 0.2)
- ARIMA (
Limitations
- Requires sufficient historical data (at least 1–2 years of daily sales).
- LSTM model may overfit with small datasets.
- External events (holidays, promotions, economic shocks) are not explicitly modeled.
Future Work
- Add exogenous features (holidays, weather, promotions).
- Compare with hybrid models (Prophet + LSTM, ARIMA + XGBoost).
- Deploy as an API for real-time forecasting.
Citation
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