Seasonal Adjustment Calculator Formula
Understand the math behind the seasonal adjustment calculator. Each variable explained with a worked example.
Formulas Used
Seasonally Adjusted Value
adjusted = observed / seasonal_indexSeasonal Effect
seasonal_effect = observed - (observed / seasonal_index)Seasonal Effect (%)
pct_seasonal = (seasonal_index - 1) * 100Variables
| Variable | Description | Default |
|---|---|---|
observed | Observed Value | 150 |
seasonal_index | Seasonal Index | 1.25 |
How It Works
How to Seasonally Adjust Data
Formula
Adjusted Value = Observed Value / Seasonal Index
Seasonal adjustment removes predictable seasonal patterns from data, revealing the underlying trend. A seasonal index above 1 means the season inflates the value; below 1 means it deflates it. Dividing by the index normalizes the value as if there were no seasonal effect.
Worked Example
December sales are $150 with a seasonal index of 1.25 (holiday boost).
- 01Adjusted = 150 / 1.25 = 120
- 02Seasonal effect = 150 - 120 = 30
- 03The seasonal boost accounts for $30 (25%) of the observed value
- 04The underlying (de-seasonalized) value is $120
Frequently Asked Questions
How are seasonal indices calculated?
Typically by computing the ratio of each period's value to the moving average centered on that period, then averaging these ratios across multiple years. The indices should average to 1.0 across all seasons.
Why is seasonal adjustment important?
It allows meaningful comparison across periods. Without adjustment, December retail sales always look great and January looks bad, obscuring the real trend. Government statistics (GDP, unemployment) are usually reported seasonally adjusted.
Is multiplicative the only seasonal model?
No. Additive seasonal adjustment subtracts the seasonal component instead of dividing. Multiplicative models are used when seasonal variation grows with the level of the series; additive when it is constant.
Ready to run the numbers?
Open Seasonal Adjustment Calculator