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language: en |
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license: mit |
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tags: |
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- time-series |
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- forecasting |
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- sales |
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- lstm |
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- arima |
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datasets: |
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- custom |
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metrics: |
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- rmse |
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- mae |
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--- |
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# 📈 Retail Sales Forecasting with ARIMA and LSTM |
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## Model Details |
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This project compares two forecasting approaches for retail sales prediction: |
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- **ARIMA (AutoRegressive Integrated Moving Average)** |
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- **LSTM (Long Short-Term Memory neural network)** |
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The models were trained and evaluated using a **rolling window evaluation** across 40 windows. Both models were assessed using RMSE, MAE, and stability metrics. |
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**Frameworks used:** |
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- ARIMA: `statsmodels`, `pmdarima` |
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- LSTM: `TensorFlow / Keras` |
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--- |
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## Evaluation Summary |
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| Model | Avg RMSE | Std RMSE | Avg MAE | Std MAE | Min RMSE | Max RMSE | |
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|-------|----------|----------|---------|---------|----------|----------| |
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| **ARIMA** | 3,175,011.32 | 763,036.27 | 2,448,829.54 | 950,375.79 | 2,195,796.46 | 6,171,402.14 | |
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| **LSTM** | 3,169,389.04 | 729,371.84 | 2,435,767.99 | 912,025.28 | 2,252,916.59 | 6,016,384.05 | |
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🏆 **Winner: LSTM** – better generalization and stability. |
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## Short Report: Model Generalization Discussion |
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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**). |
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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. |
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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. |
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**Conclusion:** |
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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. |
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## Intended Use |
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- **Task:** Time Series Forecasting (Daily Retail Sales Prediction) |
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- **Domain:** Retail / E-commerce demand forecasting |
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- **Forecast Horizon:** 30 days |
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This model can be applied to **predict daily sales**, assist in **inventory management**, **staff scheduling**, and **strategic planning**. |
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## Training Procedure |
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- **Dataset:** Rossmann-like retail sales dataset (merged `train.csv` + `store.csv`) |
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- **Preprocessing:** |
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- Removed closed days and zero-sales days |
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- Aggregated to daily level |
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- Scaled features for LSTM |
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- **Models:** |
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- ARIMA (`pmdarima.auto_arima`) |
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- LSTM with 3 stacked layers (25 units each, dropout 0.2) |
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## Limitations |
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- Requires sufficient historical data (at least 1–2 years of daily sales). |
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- LSTM model may overfit with small datasets. |
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- External events (holidays, promotions, economic shocks) are not explicitly modeled. |
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## Future Work |
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- Add exogenous features (holidays, weather, promotions). |
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- Compare with hybrid models (Prophet + LSTM, ARIMA + XGBoost). |
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- Deploy as an API for real-time forecasting. |
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--- |
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## Citation |
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If you use this model, please cite: |
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