stats (version 3.3)

decompose: Classical Seasonal Decomposition by Moving Averages

Description

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

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.

Value

  • An object of class "decomposed.ts" with following components:
  • xThe original series. (Only since R2.14.0.)
  • seasonalThe seasonal component (i.e., the repeated seasonal figure).
  • figureThe estimated seasonal figure only.
  • trendThe trend component.
  • randomThe remainder part.
  • typeThe value of type.

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.

This only works well if x covers an integer number of complete periods.

References

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

See Also

stl

Examples

Run this code
require(graphics)

m <- decompose(co2)
m$figure
plot(m)

## example taken from Kendall/Stuart
x <- c(-50, 175, 149, 214, 247, 237, 225, 329, 729, 809,
       530, 489, 540, 457, 195, 176, 337, 239, 128, 102, 232, 429, 3,
       98, 43, -141, -77, -13, 125, 361, -45, 184)
x <- ts(x, start = c(1951, 1), end = c(1958, 4), frequency = 4)
m <- decompose(x)
## seasonal figure: 6.25, 8.62, -8.84, -6.03
round(decompose(x)$figure / 10, 2)

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