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

Seasonal decomposition using moving averages

  • x (array-like) – Time series. If 2d, individual series are in columns.

  • model (str {"additive", "multiplicative"}) – Type of seasonal component. Abbreviations are accepted.

  • filt (array-like) – The filter coefficients for filtering out the seasonal component. The concrete moving average method used in filtering is determined by two_sided.

  • freq (int, optional) – Frequency of the series. Must be used if x is not a pandas object. Overrides default periodicity of x if x is a pandas object with a timeseries index.

  • two_sided (bool) – 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_trend (int 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.


results – A object with seasonal, trend, and resid attributes.

Return type



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 seasonal component is first removed by applying a convolution filter to the data. The average of this smoothed series for each period is the returned seasonal component.

See also

statsmodels.tsa.filters.bk_filter.bkfilter, statsmodels.tsa.filters.cf_filter.xffilter, statsmodels.tsa.filters.hp_filter.hpfilter, statsmodels.tsa.filters.convolution_filter