Time Series Decomposition Calculator

This calculator fits a straight line — ordinary least-squares regression — through the twelve monthly values to extract Trend Slope and Trend Intercept (lines 14-22), then derives a Seasonal component from how far each month's actual value sits from that trend line: subtracted for Additive mode, divided for Multiplicative mode (lines 31-41), and normalized so the additive seasonal component averages to 0 or the multiplicative one averages to 1 (lines 44-54). A well-known property of ordinary least-squares regression falls straight out of this: Average Trend Value always equals the simple average of the twelve monthly inputs exactly, because a fitted regression line always passes through the mean of its x- and y-values — verified directly against the engine (a 164.17 average input produces a 164.17 Average Trend Value). December and January sit at the two extreme-leverage endpoints of the OLS slope formula — month index 12 and month index 1 are tied for the largest distance from the series' midpoint, and therefore the largest weight in the slope calculation — but December's default value (140) exceeds January's (120), and with leverage tied, whichever of the two starts from the larger number ends up moving Trend Slope more when the same percentage change is applied to both, which is why December edges out January.

Seasonal Strength is computed through a decompositionType-gated ternary whose two branches are textually identical (lines 71-73) — both evaluate maxSeasonal minus minSeasonal regardless of mode — so the difference you actually see between Additive and Multiplicative Seasonal Strength comes entirely from maxSeasonal and minSeasonal themselves differing upstream, not from anything mode-specific at that particular line. This calculator does not detect or adjust for a seasonal pattern that shifts partway through the year — it fits one trend line and one fixed seasonal index per month across the whole twelve-month window.