# decompose

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##### Classical Seasonal Decomposition by Moving Averages

Decompose a time series into seasonal, trend and irregular components using moving averages. Deals with additive or multiplicative seasonal component.

Keywords
ts
##### Usage
decompose(x, type = c("additive", "multiplicative"), filter = NULL)
##### Arguments
x
A time series.
type
The type of seasonal component. Can be abbreviated.
filter
A vector of filter coefficients in reverse time order (as for AR or MA coefficients), used for filtering out the seasonal component. If NULL, a moving average with symmetric window is performed.
##### Details

The additive model used is: $$Y_t = T_t + S_t + e_t$$ The multiplicative model used is: $$Y_t = T_t\,S_t\, e_t$$ The function first determines the trend component using a moving average (if filter is NULL, a symmetric window with equal weights is used), and removes it from the time series. Then, the seasonal figure is computed by averaging, for each time unit, over all periods. The seasonal figure is then centered. Finally, the error component is determined by removing trend and seasonal figure (recycled as needed) from the original time series.

##### Value

• An object of class "decomposed.ts" with following components:
• seasonalThe seasonal component (i.e., the repeated seasonal figure)
• figureThe estimated seasonal figure only
• trendThe trend component
• randomThe remainder part
• typeThe value of type

##### Note

This function is identical to the decompose function in the stats package except that the seasonal component is not incorrectly truncated.

##### References

M. Kendall and A. Stuart (1983) The Advanced Theory of Statistics, Vol.3, Griffin, 410--414.

decompose

##### Aliases
• decompose
• plot.decomposed.ts
##### Examples
m <- decompose(co2)
plot(m)
Documentation reproduced from package forecast, version 2.19, License: GPL (>= 2)

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