# 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

 `1` ```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

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.

## Value

An object of class `"decomposed.ts"` with following components:

 `x` The original series. `seasonal` The seasonal component (i.e., the repeated seasonal figure). `figure` The estimated seasonal figure only. `trend` The trend component. `random` The remainder part. `type` The value of `type`.

## Note

The function `stl` provides a much more sophisticated decomposition.

## Author(s)

David Meyer David.Meyer@wu.ac.at

## References

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

`stl`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14``` ```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) ```