Trend+Season+Resid = y
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
About this calculator
The additive decomposition calculator splits a time series into three core components: trend, seasonality, and residuals. This method adds the elements to reconstruct the original series, represented by the formula: y = Trend + Seasonality + Residuals. It helps analyze long-term patterns (trend), recurring cycles (seasonality), and random fluctuations (residuals).
It models the trend as a smooth curve, seasonality as periodic oscillations, and residuals as unexplained variations. Best suited for data where seasonal variations have constant amplitude, such as sales during fixed holidays or energy consumption across seasons.
Before applying this method, ensure the series is stationary in trend and seasonality. Additive decomposition is not ideal when seasonal variations increase over time. Always analyze residuals to detect anomalies or outliers.
Frequently asked questions
When should I use additive vs multiplicative decomposition?
Use additive when seasonal variations maintain constant amplitude over time. Multiplicative is better for data where seasonal fluctuations grow with the series level.
What does the residual component represent?
Residuals are what remains after removing trend and seasonality. They indicate anomalies, noise, or model errors.
Can this calculator handle irregular time intervals?
No. Additive decomposition requires data collected at regular intervals, such as daily, weekly, or monthly.
How to interpret negative seasonality values?
Negative seasonality values mean the series level is below the expected trend for that period.