Calculator Inputs
Example Data Table
This sample shows an upward trend with a yearly cycle.
| Label | Value |
|---|---|
| 2024-01 | 120 |
| 2024-02 | 128 |
| 2024-03 | 135 |
| 2024-04 | 142 |
| 2024-05 | 150 |
| 2024-06 | 160 |
| 2024-07 | 172 |
| 2024-08 | 168 |
| 2024-09 | 155 |
| 2024-10 | 145 |
| 2024-11 | 138 |
| 2024-12 | 148 |
| 2025-01 | 125 |
| 2025-02 | 132 |
| 2025-03 | 140 |
| 2025-04 | 148 |
| 2025-05 | 156 |
| 2025-06 | 166 |
| 2025-07 | 180 |
| 2025-08 | 175 |
| 2025-09 | 162 |
| 2025-10 | 152 |
| 2025-11 | 145 |
| 2025-12 | 155 |
Formula Used
This tool applies classical seasonal decomposition using a centered moving average trend and seasonal indices by position.
How to Use This Calculator
- Paste your observations in the data box, one row per time step.
- If you have dates or labels, use the label,value format.
- Set the season length (period), such as 12 for monthly data.
- Pick additive for constant seasonal swings, multiplicative for proportional swings.
- Click Decompose Series to see results under the header.
- Use the download buttons to export your tables for reports.
Data structure and input quality
Seasonal decomposition assumes observations arrive at regular intervals, such as sales, weekly defects, or monthly energy usage. For stability, provide at least two full seasons; with a 12-step period, 24 to 36 points improves index averaging. Keep units consistent, remove duplicated timestamps, and review one-off spikes as special events. Missing points can be written as NA and handled by skipping or interpolating internal gaps.
Season length and moving-average coverage
The period controls seasonal grouping and the trend smoother. Trend is estimated with a centered moving average of length m. When m is even, a second centering step aligns the trend to integer positions, so edge values can be unavailable. Use n ≥ 2m for a workable output in practice, and n ≥ 3m for steadier indices. Example: n=36 with m=12 yields a trend for most months and clearer seasonality.
Model choice: additive versus multiplicative
Choose additive when seasonal swings have constant magnitude, for example ±15 units regardless of baseline. Choose multiplicative when swings scale with the level, such as +8% in peak months and −6% in off months. Multiplicative decomposition requires positive observations because it uses ratios. Indices are normalized so additive indices sum to zero per period, while multiplicative indices average to one, easing cross-series comparison for clearer interpretation.
Diagnostics that support reliable reporting
Residual diagnostics summarize what remains after removing trend and seasonality. Additive residuals should have a mean near 0 and a stable spread; multiplicative residuals should cluster around 1. Seasonal strength approaches 1 when residual variance is small relative to detrended variance. Fit metrics quantify accuracy on fitted points: MAE is typical absolute error, RMSE penalizes large misses, and MAPE expresses percentage error when observed values are nonzero.
Using components for forecasting workflows
Use the deseasonalized series to model underlying movement with regression, smoothing, or autoregressive methods, then reapply seasonal indices to reconstruct forecasts. Compare fitted and observed values to spot regime changes, and monitor residuals for unusual cycles or breaks. If residual mean drifts or error metrics rise, revisit the period and model, or add external drivers. Export the component table to share key assumptions and reproducible calculations with stakeholders.
FAQs
How do I choose the season length (period)?
Match the period to the repeating cycle in your sampling. Monthly data often uses 12, daily data with weekly seasonality uses 7, and quarterly series uses 4. If unsure, test nearby values and compare error metrics.
Why is the trend sometimes shown as a dash at the edges?
Centered moving averages need points on both sides of a time step. Near the beginning and end, the full window is unavailable, so the trend is intentionally left blank to avoid biased estimates.
Should I skip missing values or interpolate them?
Skip is safer when gaps are large or irregular. Interpolation is helpful for small internal gaps because it restores continuity for the moving average. Avoid interpolation when missingness is systematic or when values jump abruptly.
When is a multiplicative model appropriate?
Use multiplicative when seasonal effects scale with the level, such as percentage swings. All observations must be positive because the method uses ratios. If your data includes zeros or negatives, choose additive.
What does seasonal strength indicate?
Seasonal strength summarizes how much variation remains seasonal after accounting for trend. Values closer to 1 suggest a strong, consistent seasonal pattern, while values near 0 suggest weak seasonality or high residual noise.
What do the CSV and PDF downloads include?
Exports use the component table displayed in results: label, observed, trend, seasonal, fitted, residual, and deseasonalized values. The PDF is a formatted landscape report, and the CSV is a raw file for analysis tools.