A seasonal index is a number that says how much a particular season is above or below the yearly average. 1.4 means that season is typically 40% above average, 0.6 means 40% below. The indices always average to 1 (or sum to the number of seasons).
Deseasonalise (remove the season to see the true trend): actual ÷ SI.
Forecast / reseasonalise (put the season back onto a trend value): trend × SI.
Season means: Summer 154, Autumn 110, Winter 66, Spring 110. The overall mean is 110. Find each seasonal index.
| Season | Mean ÷ 110 | SI |
|---|---|---|
| Summer | 154 ÷ 110 | 1.4 |
| Autumn | 110 ÷ 110 | 1.0 |
| Winter | 66 ÷ 110 | 0.6 |
| Spring | 110 ÷ 110 | 1.0 |
Check: 1.4 + 1.0 + 0.6 + 1.0 = 4 ✓ (they sum to the number of seasons, so they average to 1).
• Deseasonalise = ÷ SI. Forecast = × SI. Mixing these up is the classic lost mark.
• Seasonal indices must add to the number of seasons (4 for quarters, 12 for months).
• SI above 1 = a busy season, below 1 = a quiet season.
• A missing index = (number of seasons) − (sum of the others).
Summer sits 40% above the dashed average line (1.4), winter 40% below (0.6), autumn and spring are bang on average (1.0). They balance out around 1.
Going in to see the true trend, divide. Coming back out to predict a real figure, multiply.
Don't read yet, just have a go in your head:
Summer mean 154, overall mean 110. SI = 154 ÷ 110 = 1.4 (40% above average).
Winter mean 66, overall mean 110. SI = 66 ÷ 110 = ? → that's ?% below average.
Winter's actual sales were 84, and winter's SI is 0.6. Deseasonalise this figure. Check below.
The trend predicts a value of 120 for next summer, and summer's SI is 1.4. Forecast the actual summer figure.
In one sentence, out loud: when do you divide by the seasonal index, and when do you multiply?