Break down a time series into its core components using the Decomposition Calculator. Enter your data values, select a period (e.g. 4 for quarterly, 12 for monthly), and choose between additive or multiplicative decomposition. You get back the trend, seasonal, and residual components for each data point, plus a breakdown chart showing how the series is structured.
Data Points Analyzed
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Average Trend Value
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Seasonal Strength Index
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Residual Variance
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Time series decomposition is a statistical technique that separates a time series into its fundamental components: trend (long-term direction), seasonal (repeating periodic patterns), and residual (random noise or irregular variation). This makes it easier to analyze and forecast future values.
In additive decomposition, the components are summed: Original = Trend + Seasonal + Residual. This works best when seasonal fluctuations remain constant in magnitude over time. Multiplicative decomposition multiplies them: Original = Trend × Seasonal × Residual, and is better suited when seasonal variation grows proportionally with the trend level.
The period is the number of observations in one complete seasonal cycle. Use 12 for monthly data with yearly seasonality, 4 for quarterly data, 7 for daily data with weekly seasonality, or 52 for weekly data with yearly seasonality. Choosing the right period is critical for meaningful decomposition.
The trend is estimated using a centered moving average (CMA) of length equal to the period. For even-period data, a 2×m moving average is applied to center the trend correctly. This smooths out seasonal and irregular fluctuations to reveal the underlying long-term direction.
Once the trend is computed, it is removed from the original data (subtracted for additive, divided for multiplicative). The resulting de-trended values are then averaged by their position within the season (e.g., all January values averaged together), producing a single representative seasonal index for each position in the cycle.
The residual (also called the irregular or error component) is what remains after the trend and seasonal components are removed. Ideally it should appear as random noise with no discernible pattern. Large or structured residuals may indicate that the model is missing an important component or that the chosen period is incorrect.
The centered moving average requires half a period's worth of data on each side of every point. As a result, the first and last ⌊period/2⌋ observations cannot have a trend value calculated, and those cells will appear blank. This is normal behavior for classical decomposition.
You need at least two full seasonal cycles — so a minimum of 2 × period data points. For example, monthly data requires at least 24 observations. More data generally produces more stable and reliable trend and seasonal estimates.