Seasonality Strength Results
| Period | Index | Effect | Avg Raw | Obs | Std | 95% CI Low | 95% CI High |
|---|
Calculator Inputs
Formula Used
The tool measures recurring seasonal behavior after optional detrending. It reports a strength score using between-period variance share and a stability component.
Linear trend (optional): y_t = a + b t
Multiplicative detrended value: d_t = (x_t / trend_t) * 100
Additive detrended value: d_t = x_t - trend_t
Seasonal index for period p: S_p = average(d_t for all t in period p)
Normalized multiplicative index: S'_p = S_p * (100 / average(S_p))
Normalized additive index: S'_p = S_p - average(S_p)
ANOVA seasonality share (eta²): eta² = SS_between / SS_total
Final strength score: 0.7 × (eta² × 100) + 0.3 × stability_score
Stability score is derived from average within-period variability (lower variability increases stability).
How to Use This Calculator
- Paste your time-series values into the first box.
- Set Periods per Cycle (monthly = 12, quarterly = 4, weekly pattern = 7).
- Choose a seasonality model and detrending method.
- Optionally add custom seasonal names and labels for charts.
- Click Calculate Seasonality Strength to show the result above the form.
- Review the summary cards, charts, and seasonal index table.
- Export results using the CSV or PDF buttons.
Example Data Table
24 monthly observationsThis sample includes two years of monthly values with visible seasonality. Use the Load Example Data button to test the calculator.
| Year | Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 2024 | 120 | 128 | 142 | 158 | 172 | 190 | 214 | 208 | 184 | 166 | 150 | 138 |
| 2025 | 132 | 141 | 156 | 172 | 188 | 207 | 233 | 226 | 199 | 180 | 162 | 149 |
Seasonality Score Interpretation
The calculator combines ANOVA seasonality share and a stability score to produce a 0 to 100 result. Scores above 60 usually indicate repeatable timing patterns, while scores below 40 suggest weaker periodic behavior. Teams can compare monthly sales, website sessions, or support tickets using the same framework. Because the score separates recurring structure from trend movement, it supports cleaner forecasting discussions and more consistent reporting across departments.
Cycle Design and Data Depth
Periods per cycle define the pattern lens. Monthly business data uses 12 periods, quarter based series use 4, and weekday operations often use 7. The tool works with one cycle, but two or more full cycles produce stronger estimates. With 24 monthly observations, each seasonal bucket receives two data points, acceptable for exploration. More cycles improve confidence intervals, reduce sensitivity to outliers, and make seasonal index comparisons more reliable.
Detrending Choices and Quality Control
Linear regression detrending fits a trend line and is usually best for short datasets with gradual growth. Moving average detrending helps when the baseline shifts unevenly, but edge gaps can appear when the window is large. The winsorization option caps extreme detrended values so one shock does not distort seasonal indices. Analysts should test both detrending methods and review warnings before using results in budgets, staffing, or demand planning decisions.
Reading Seasonal Index Outputs
In multiplicative mode, normalized indices center around 100. A period index of 118 indicates performance runs about 18 percent above the baseline, while 92 indicates an 8 percent shortfall. The peak to trough swing summarizes amplitude and helps prioritize operational responses. Confidence intervals show whether differences are likely meaningful or noise. A narrow interval around peak months supports marketing timing, inventory positioning, and campaign launch scheduling.
Operational Use Cases and Reporting
This tool supports recurring analysis in retail, SaaS, logistics, education, and healthcare. Finance teams can export CSV files for model inputs, while managers can save PDF summaries for reviews. A practical workflow is to calculate the strength score monthly, track changes in peak periods, and monitor stability deterioration. When strength falls sharply, it may signal product mix changes, policy shifts, or data quality issues requiring investigation.
FAQs
1. What does the strength score measure?
It summarizes how strongly recurring seasonal timing appears after detrending. The score blends between-period separation and within-period consistency, so higher values indicate clearer and more stable seasonality.
2. When should I use multiplicative mode?
Use multiplicative mode when seasonal effects scale with the level, such as sales growing over time while percentage seasonality remains similar. Indices will center around 100 for easier interpretation.
3. When is additive mode better?
Additive mode is better when seasonal impact is a roughly fixed amount, not a percentage. This often fits counts or volumes where peak periods add similar units each cycle.
4. How many observations are recommended?
Two or more full cycles are recommended for more stable indices and confidence intervals. You can test one cycle, but results are more sensitive to outliers and temporary shocks.
5. What does winsorization do?
Winsorization caps extreme detrended values at selected percentile limits. It reduces the impact of unusual spikes or drops so one event does not dominate the seasonal pattern estimate.
6. Why are some trend values missing?
Missing trend values usually occur with moving average detrending near the start and end of the series. Linear regression detrending avoids those edge gaps and often works better on short datasets.