# Seasonal Decompose Interpretation

Q1) How to interpret the Seasonal Decompose (Additive V/S Multiplicative) plotted against the same dataset?

Q2) And, on the basis of the below plotted Observed data-points, which decomposition one makes more sense, and why?

Observations from Multiplicative Decomposition:

• Seasonal & Trend chart scales between 0.99 to 1.00

• Seasonal chart scales between -3 to 3
• Trend chart scales between -2 to 2

Code Used:

import statsmodels.datasets.co2 as co2
co2_data = co2_data.fillna(co2_data.interpolate()); co2_data.columns=["co2_interpolated"]

y = co2_data["co2_interpolated"]

decomposition_mul = sm.tsa.seasonal_decompose(y, model='multiplicative')


Plot:

def plotseasonal(res, axes, title):
axes[0].title.set_text(title)
res.observed.plot(ax=axes[0], legend=False)
axes[0].set_ylabel('Observed')

res.trend.plot(ax=axes[1], legend=False)
axes[1].set_ylabel('Trend')

res.seasonal.plot(ax=axes[2], legend=False)
axes[2].set_ylabel('Seasonal')

res.resid.plot(ax=axes[3], legend=False)
axes[3].set_ylabel('Residual')

fig, axes = plt.subplots(ncols=2, nrows=4, sharex=False, figsize=(30,15))
plotseasonal(decomposition_mul, axes[:,0], title="Multiplicative")
$$$$
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1. An additive component is added to "everything else" (which usually means "to the baseline and trend, and anything left over is noise), and a multiplicative component is multiplied by "everything else". In your plots, the additive component adds $$\pm 3$$ units, while a multiplicative component changes "everything else" by $$\pm 0.9\%$$.