| Month | Value | Month | Value |
|---|---|---|---|
| 2024-01 | 120 | 2025-01 | 130 |
| 2024-02 | 128 | 2025-02 | 138 |
| 2024-03 | 142 | 2025-03 | 152 |
| 2024-04 | 150 | 2025-04 | 160 |
| 2024-05 | 160 | 2025-05 | 170 |
| 2024-06 | 155 | 2025-06 | 165 |
| 2024-07 | 148 | 2025-07 | 158 |
| 2024-08 | 152 | 2025-08 | 162 |
| 2024-09 | 165 | 2025-09 | 176 |
| 2024-10 | 172 | 2025-10 | 184 |
| 2024-11 | 180 | 2025-11 | 192 |
| 2024-12 | 210 | 2025-12 | 225 |
- Multiplicative: R(t) = y(t) / MA(t)
- Additive: D(t) = y(t) − MA(t)
- Multiplicative: Adj(t) = y(t) / S(pos)
- Additive: Adj(t) = y(t) − S(pos)
- Paste values, one per line, or use label,value.
- Set season length m (e.g., 12 for monthly).
- Choose centered smoothing for better alignment.
- Select multiplicative or additive seasonality when appropriate.
- Optionally set a forecast horizon for seasonal-naive projections.
- Press Calculate to view tables and charts.
Choosing the right season length
Season length m defines repeating structure, such as 12 months, 4 quarters, or 7 days. With 24 monthly points, m=12 gives two full cycles, enough to estimate stable seasonal factors and reduce noise. If you are unsure, check calendar logic first, then confirm with an autocorrelation peak at lag m.
Centered smoothing for cleaner seasonality
A centered moving average aligns the window around each period, limiting phase shift. For odd m, the window is symmetric; for even m, two adjacent m-window means are averaged to center the series. In practice, centered smoothing produces a better “trend-cycle” baseline, so seasonal ratios are not distorted by timing offsets.
Ratio-to-moving-average seasonal factors
Multiplicative seasonality uses R(t)=y(t)/MA(t), capturing proportional swings. Additive seasonality uses D(t)=y(t)−MA(t), capturing absolute lifts. The calculator normalizes multiplicative factors to mean 1 and additive factors to mean 0 for interpretability. When values can be near zero, additive factors are often safer because ratios can explode.
Seasonally adjusted values for trend work
Adjusted values remove repeating effects: Adj(t)=y(t)/S(pos) or Adj(t)=y(t)−S(pos). This makes trend and regime changes visible, supports anomaly screening, and stabilizes variance for downstream modeling such as regression or state space methods. A common workflow is to model the adjusted series, then reapply the seasonal factor to return forecasts to original units.
Edge effects and data sufficiency
Moving averages are undefined near the boundaries because windows are incomplete. Expect missing MA values at the start and end, roughly m/2 points for centered methods. Provide at least one full season; two seasons improve robustness and reduce factor leakage. If data is sparse, consider reducing m or aggregating to a coarser frequency so each season has enough observations.
Seasonal-naive forecasting with factors
Forecasts here combine a level estimate with seasonal position. With decomposition enabled, level is the mean of the last m adjusted values. Forecasts are level×S(pos) for multiplicative or level+S(pos) for additive. Use horizons that match planning cycles, for example 4 weeks for staffing or 12 months for budgeting, and review shocks before trusting horizons.
FAQs
1) What is a seasonal moving average used for?
It smooths a time series while respecting a repeating pattern. You get a trend-cycle baseline, seasonally adjusted values, and simple factor-based forecasts that are easier to interpret than raw, noisy observations.
2) How do I choose the season length m?
Pick the number of periods in one full cycle: 12 for monthly yearly seasonality, 4 for quarterly, 7 for daily weekly. If unsure, test likely m values and prefer the one that yields stable factors across cycles.
3) Should I use multiplicative or additive seasonality?
Use multiplicative when seasonal swings scale with the level, such as demand growing and shrinking by percentages. Use additive when the seasonal effect is a roughly constant offset. If values approach zero, additive is usually safer.
4) Why are some moving average cells blank?
At the boundaries, a full window is unavailable, so the moving average cannot be computed. Centered smoothing typically leaves about m/2 missing points at each end. This is expected and does not indicate a calculation error.
5) How are the forecasts calculated?
The tool estimates a level from the last m seasonally adjusted values, then projects future periods using their seasonal position. Forecasts are level×factor for multiplicative or level+factor for additive. With no decomposition, it forecasts the level only.
6) Can I download and reuse the results?
Yes. Download CSV for spreadsheets and pipelines, or PDF for sharing and reporting. Labels you provide (such as dates) are preserved in exports, and the chart reflects the same calculated series and forecasts.