Executive Summary
Key forecast and model performance metrics
Demand forecast fitted on 2000 observations aggregated into 365 time periods. ARIMA model achieved RMSE of 2.54 units with AIC 1725.95. Promotional campaigns show average lift of 0.7% in demand.
Demand Trend Over Time
Historical demand trajectory showing overall trend and seasonal patterns
Demand over the historical period ranges from 4.2 to 35.8 units, with mean of 19.8. The trajectory shows downward pattern with 365 observations.
Seasonal Decomposition
Decomposition of demand into trend, seasonal, and irregular components
Seasonal decomposition reveals trend explains 90.7% of variation. Seasonal component shows weak patterns. Remainder (irregular variation) has sd 2.39.
Demand Forecast with Confidence Intervals
Point forecast and 95% prediction intervals for future demand
Forecast for the next 3 periods averages 19.3 units. Prediction interval width (95% confidence) ranges from 14.2 to 24.3 units, indicating high uncertainty.
Average Demand by Region
Average demand across geographic regions
Regional demand varies from 19.4 to 20.2 units, with North showing highest demand at 20.2 units. All 4 regions analyzed.
Promotion Impact Summary
Estimated demand lift from promotional campaigns
| Metric | Value |
|---|---|
| Mean Demand (With Promotion) | 23.86 |
| Mean Demand (Without Promotion) | 19.35 |
| Promotion Lift (%) | 0.7 |
| Observations (With Promotion) | 205 |
| Observations (Without Promotion) | 1795 |
Promotional periods show average demand of 23.9 units vs 19.4 units without promotion—a lift of 0.7%. Analysis based on 205 promotional observations and 1795 non-promotional periods.
Inventory Level vs Demand
Relationship between current inventory levels and demand realized
Inventory and demand show correlation of -0.055 across 2000 observations. Lower inventory levels are weakly associated with higher demand, suggesting proactive stock planning.
Model Diagnostics: Fitted vs Residuals
Scatter plot of fitted values against residuals to assess model fit quality
Residuals scatter around zero with mean -1.80e-02 and std dev 2.54. No clear trend pattern visible, suggesting good quality model specification.
Residual Distribution
Distribution of model residuals to assess normality assumption
Residuals (n=365) have mean -1.80e-02 and standard deviation 2.54. Distribution appears approximately normal (Shapiro-Wilk p > 0.05).
Forecast Accuracy Metrics
In-sample model fit statistics and forecast error measures
| Metric Name | Metric Value |
|---|---|
| RMSE (Root Mean Squared Error) | 2.54 |
| MAE (Mean Absolute Error) | 2 |
| MAPE (Mean Absolute Percentage Error) | 11.93% |
| AIC (Akaike Information Criterion) | 1725.95 |
| BIC (Bayesian Information Criterion) | 1749.33 |
| Number of Observations | 2000 |
| Number of Aggregated Periods | 365 |
Model fit assessed via AIC (1725.95) and BIC (1749.33). Forecast accuracy shows RMSE 2.54, MAE 2.00, and MAPE 11.93%, indicating good forecast quality.