| % 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} |