After decomposing the time series, what is the intuitive difference between seasonality-adjusted data and the trend component (from decomposition)?
1 Answer
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An additive time series decomposition expresses a time series as $$y_t = T_t + S_t + R_t$$ where $T_t$ is the trend component, $S_t$ is the seasonal component and $R_t$ is the remainder.
The seasonally adjusted series is given by $y_t - S_t = T_t + R_t$. That is, it is equal to the sum of the trend and remainder components.
See https://otexts.com/fpp3/components.html for more details.
answered Sep 12, 2022 at 6:47