statsmodels.tsa.seasonal.seasonal_decompose(x, model='additive', filt=None, period=None, two_sided=True, extrapolate_trend=0)[source]

Seasonal decomposition using moving averages.


Time series. If 2d, individual series are in columns. x must contain 2 complete cycles.

model{“additive”, “multiplicative”}, optional

Type of seasonal component. Abbreviations are accepted.

filtarray_like, optional

The filter coefficients for filtering out the seasonal component. The concrete moving average method used in filtering is determined by two_sided.

periodint, optional

Period of the series (eg, 1 for annual, 4 for quarterly, etc). Must be used if x is not a pandas object or if the index of x does not have a frequency. Overrides default periodicity of x if x is a pandas object with a timeseries index.

two_sidedbool, optional

The moving average method used in filtering. If True (default), a centered moving average is computed using the filt. If False, the filter coefficients are for past values only.

extrapolate_trendint or ‘freq’, optional

If set to > 0, the trend resulting from the convolution is linear least-squares extrapolated on both ends (or the single one if two_sided is False) considering this many (+1) closest points. If set to ‘freq’, use freq closest points. Setting this parameter results in no NaN values in trend or resid components.


A object with seasonal, trend, and resid attributes.

See also


Baxter-King filter.


Christiano-Fitzgerald asymmetric, random walk filter.


Hodrick-Prescott filter.


Linear filtering via convolution.


Season-Trend decomposition using LOESS.


This is a naive decomposition. More sophisticated methods should be preferred.

The additive model is Y[t] = T[t] + S[t] + e[t]

The multiplicative model is Y[t] = T[t] * S[t] * e[t]

The results are obtained by first estimating the trend by applying a convolution filter to the data. The trend is then removed from the series and the average of this de-trended series for each period is the returned seasonal component.

Last update: Jun 14, 2024