decompose
Classical Seasonal Decomposition by Moving Averages

Description

Decomposes a time series object by moving averages into seasonal, tread and random components.

Usage

decompose(x, type = c("additive", "multiplicative"), filter = NULL)

Arguments

x a time series object with an integral frequency greater than one (so it has a seasonal component).
type a character string, "additive" or "multiplicative", specifying the type of decomposition. Partial character string matching is allowed.
filter a vector of filter coefficients used to filter out the seasonal component. If NULL, a centered filter of frequency(x) weights of 1/frequency(x) is used (if frequency(x) is even then the default filter is extended by 1 and the outermost weights are 1/(2*frequency(x))).

Details

A time series object will first be filtered to get the trend component and then the tread component will be removed from the data (by subtraction or division, depending on the type of decomposition). The seasonal figure is the period average for each time unit, centered by subtraction or division by its mean so that its mean is 0 (additive) or 1 (multiplicative). Finally, the random component is computed by removing trend and seasonal figure from the original time series.
For additive decomposition, X[i] = T[i] + S[i] + R[i]
For multiplicative decomposition, X[i] = T[i] * S[i] * R[i]
where X, T, S, R are original time series, tread, seasonal and random component, respectively.
Value
A list object of class "decomposed.ts" with components:

x the original time series.
seasonal the seasonal component.
tread the tread component.
random the random component.
figure the vector of seasonal figure. (This starts at the starting time of x, not at the start of a period.)
type the type of decomposition, "additive" or "multiplicative".
See Also
filter, ts
Examples
qtlySales <- ts(c(3.4, 3.9, 3.5, 3.0, 3.7, 4.2, 3.7, 3.4, 3.8, 4.5), start=2013.25, frequency=4)
decompose(qtlySales)
decompose(qtlySales, type="multiplicative")$figure
Package stats version 6.1.1-7
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