# ARIMA Model for M5 Demand Forecasting

## Overview
AutoRegressive Integrated Moving Average trained on aggregated daily M5 sales data.

## Model Details
- **Architecture**: ARIMA(3,1,1) with trend
- **Training Data**: 1,913 days of aggregated daily sales
- **Test Period**: 28 days (2016-04-25 to 2016-05-22)
- **Differencing**: d=1 (first differencing required for stationarity)

## Stationarity Test
- ADF Statistic: -1.565373
- p-value: 0.500960
- Original data non-stationary; first differencing achieves stationarity

## Performance
| Metric | Value |
|--------|-------|
| RMSE | 6,459.70 |
| MAE | 4,852.62 |
| MAPE | 10.48% |
| AIC | 37,801.28 |

## Key Features
- AR component: 3 autoregressive terms
- I component: 1st order differencing (d=1)
- MA component: 1 moving average term
- Trend term: 't' (deterministic trend)

## Usage
```python
import pickle

with open('model.pkl', 'rb') as f:
    model = pickle.load(f)

forecast = model.forecast(steps=28)
```

## Notes
- Simplest model but requires manual order selection
- No seasonal component (SARIMAX handles this better)
- Good baseline but underperforms compared to Prophet and SARIMAX
- Smallest model file (6.5MB) due to no seasonal components