Additive Model
Time Series — Chapter 3, GSEB Class 12 Statistics
Two Models
There are two ways to combine the four components of a time series:
- Each component is an absolute value (not a percentage)
- Components are independent — no interaction between them
- Seasonal effect is constant in magnitude over time
- All terms measured in the same units as original data
Additive Model — Example
A shop's monthly sales (in thousands):
Trend = 120 (steady growth), Seasonal = +15 (summer boost), Cyclical = −5 (slight recession), Random = +3 (lucky week)
Y = T + S + C + R = 120 + 15 + (−5) + 3 = 133 thousand
All values in same units (thousands of rupees) — simply add them up.
When to Use Which?
| Feature | Additive | Multiplicative |
|---|---|---|
| Formula | Y = T + S + C + R | Y = T × S × C × R |
| Component type | Absolute values | Proportions/percentages |
| Seasonal effect | Constant over time | Grows with trend |
| Real-world use | Simple, stable series | Most business/economic data |
| GSEB preference | ✓ Primarily used | Mentioned for comparison |
GSEB primarily uses the additive model. If a question doesn't specify, assume additive: Y = T + S + C + R.
Key Takeaways
Key Takeaways
- Additive model: Y = T + S + C + R — components add up as absolute values.
- Multiplicative model: Y = T × S × C × R — components multiply as proportions.
- In additive, seasonal effect is constant; in multiplicative, it grows with trend.
- GSEB primarily uses the additive model for exam problems.
- All terms in additive model are in the same units as the original data.