% File src/library/stats/man/decompose.Rd
% Part of the R package, https://www.R-project.org
% Copyright 1995-2017 R Core Team
% Distributed under GPL 2 or later

\name{decompose}
\alias{decompose}
\alias{plot.decomposed.ts}
\title{
  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{
  \item{x}{A time series.}
  \item{type}{The type of seasonal component. Can be abbreviated.}
  \item{filter}{A vector of filter coefficients in reverse time order (as for
    AR or MA coefficients), used for filtering out the seasonal
    component.  If \code{NULL}, a moving average with symmetric window is
  performed.}
}
\details{
  The additive model used is:
  \deqn{Y_t = T_t + S_t + e_t}{Y[t] = T[t] + S[t] + e[t]}
  The multiplicative model used is:
  \deqn{Y_t = T_t\,S_t\, e_t}{Y[t] = T[t] * S[t] * e[t]}

  The function first determines the trend component using a moving
  average (if \code{filter} is \code{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 \code{x} covers an integer number of complete
  periods.
}
\note{
  The function \code{\link{stl}} provides a much more sophisticated
  decomposition.
}
\value{
  An object of class \code{"decomposed.ts"} with following components:
  \item{x}{The original series.}
  \item{seasonal}{The seasonal component (i.e., the repeated seasonal figure).}
  \item{figure}{The estimated seasonal figure only.}
  \item{trend}{The trend component.}
  \item{random}{The remainder part.}
  \item{type}{The value of \code{type}.}
}
\references{
  M. Kendall and A. Stuart (1983)
  \emph{The Advanced Theory of Statistics}, Vol.3,
  Griffin. pp.\sspace{}410--414.
}
\author{
  David Meyer \email{David.Meyer@wu.ac.at}
}
\seealso{\code{\link{stl}}}

\examples{
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)
}
\keyword{ts}