Time Series Decomposition
Paste a series, pick STL or the classical moving-average method, and get the trend, seasonal and residual components as a four-panel SVG — plus the component table, seasonal indices and strength diagnostics as text, CSV or JSON.
About this tool
Time series decomposition separates an evenly spaced series into the slow-moving trend, the repeating seasonal pattern, and the leftover residual. It is the quick way to answer questions like "is demand really growing, or is this just the December peak?" and "which points are unusual after accounting for the weekly cycle?"
Paste values one per line, label,value rows, or a single comma/space-separated
line. Set period when you know the cycle length — 12 for monthly data with a
yearly pattern, 4 for quarterly, 7 for daily data with a weekly pattern, 24 for
hourly data with a daily pattern — or leave it at 0 to detect the strongest
autocorrelation peak.
The default STL method uses a local smoother and can run a robust pass that keeps outliers from bending the trend. The classical method uses a centred moving average and one fixed seasonal index for each position in the cycle. Use an additive model when the seasonal swing is roughly constant, and a multiplicative model when the swing grows with the level.
Worked example
Input:
Jan,104
Feb,102
Mar,99.5
Apr,98.5
May,97
Jun,101
Jul,104.5
Aug,107
Sep,110.5
Oct,107.5
Nov,103
Dec,102.5
Jan,110
Feb,108
Mar,105.5
Apr,104.5
May,103
Jun,107
Jul,110.5
Aug,113
Sep,116.5
Oct,113.5
Nov,109
Dec,108.5
With period=12, the SVG output shows four stacked panels: observed values,
trend, seasonal component, and residual. Switch output to table, csv, or
json when you need the exact component values, seasonal indices, and the
strength-of-trend / strength-of-seasonality diagnostics.
Limits and edge cases
- Input is capped at 10,000 observations and needs at least two full seasonal
cycles. For
period=12, paste at least 24 values. - Multiplicative decomposition requires every value to be greater than zero. Use additive mode for data that can be zero or negative.
period=0uses autocorrelation and can fail on very short or trend-only series. Set the period explicitly when you know the sampling cadence.- The chart is an SVG string, so it can be copied, downloaded, or embedded in a report. No network call or plotting service is used.
FAQ
What period should I choose?
Use the number of observations in one repeating cycle. Monthly data with yearly
seasonality uses 12, quarterly uses 4, daily data with a weekly pattern uses
7, and hourly data with a daily pattern uses 24. Leave period=0 only when
you want the tool to infer the strongest cycle from autocorrelation.
When should I use STL instead of classical decomposition?
Use STL when the seasonal shape can drift over time or when you want robust
mode to isolate outliers. Use classical decomposition when you want the textbook
moving-average trend and one fixed seasonal index for each point in the cycle.
What is the difference between additive and multiplicative models?
Additive mode assumes observed = trend + seasonal + residual, so the seasonal
swing has about the same size across the whole series. Multiplicative mode
assumes observed = trend × seasonal × residual, so seasonal swings scale with
the series level; it requires strictly positive data.
Why did automatic period detection fail?
The detector looks for a strong autocorrelation peak. Trend-only data, very noisy
series, or fewer than two cycles may not have a trustworthy peak. Set period
explicitly and rerun; if the data is monthly, start with 12.
Can I export the component values?
Yes. Use output=csv for one row per observation, output=json for diagnostics
plus component arrays, or output=table for a readable text table. The SVG is
best for visual reporting; the other formats are best for downstream analysis.
Developer & Automation Access
Run it from the terminal
Same engine as this page, headless — via the gizza CLI:
gizza tool ts-decompose "2024-01,112
2024-02,118
2024-03,132
2024-04,129"New to the CLI? Get gizza →
Open it by URL
Pre-fill and auto-run this tool with query parameters — the names match the API/CLI:
https://gizza.ai/tools/ts-decompose/?data=2024-01%2C112%0A2024-02%2C118%0A2024-03%2C132%0A2024-04%2C129&method=stl&model=additive&period=12&seasonal_window=0&trend_window=0&robust=true&two_sided=true&extrapolate_trend=true&trend_overlay=true&show_adjusted=true&residual_style=bar&grid=true&title=Monthly%20sales&x_label=Month&y_label=Units%20sold&width=900&height=720&color=%232563eb&theme=light&precision=4&output=svgMachine-readable descriptor: tool.json — title + parameters JSON Schema for agents.