Decompose a time series into seasonal, trend and irregular components
using loess, acronym STL.
stl(x, s.window, s.degree = 0,
t.window = NULL, t.degree = 1,
l.window = nextodd(period), l.degree = t.degree,
s.jump = ceiling(s.window/10),
t.jump = ceiling(t.window/10),
l.jump = ceiling(l.window/10),
robust = FALSE,
inner = if(robust) 1 else 2,
outer = if(robust) 15 else 0,
na.action = na.fail)univariate time series to be decomposed.
This should be an object of class "ts" with a frequency
greater than one.
either the character string "periodic" or the span (in
lags) of the loess window for seasonal extraction, which should
be odd and at least 7, according to Cleveland et al. This has no default.
degree of locally-fitted polynomial in seasonal extraction. Should be zero or one.
the span (in lags) of the loess window for trend
extraction, which should be odd. If NULL, the default,
nextodd(ceiling((1.5*period) / (1-(1.5/s.window)))), is taken.
degree of locally-fitted polynomial in trend extraction. Should be zero or one.
the span (in lags) of the loess window of the low-pass
filter used for each subseries. Defaults to the smallest odd
integer greater than or equal to frequency(x) which is
recommended since it prevents competition between the trend and
seasonal components. If not an odd integer its given value is
increased to the next odd one.
degree of locally-fitted polynomial for the subseries low-pass filter. Must be 0 or 1.
integers at least one to increase speed of
the respective smoother. Linear interpolation happens between every
*.jumpth value.
logical indicating if robust fitting be used in the
loess procedure.
integer; the number of ‘inner’ (backfitting) iterations; usually very few (2) iterations suffice.
integer; the number of ‘outer’ robustness iterations.
action on missing values.
stl returns an object of class "stl" with components
a multiple time series with columns
seasonal, trend and remainder.
the final robust weights (all one if fitting is not done robustly).
the matched call.
integer (length 3 vector) with the spans used for the "s",
"t", and "l" smoothers.
integer (length 3) vector with the polynomial degrees for these smoothers.
integer (length 3) vector with the ‘jumps’ (skips) used for these smoothers.
number of inner iterations
number of outer robustness iterations
The seasonal component is found by loess smoothing the
seasonal sub-series (the series of all January values, …); if
s.window = "periodic" smoothing is effectively replaced by
taking the mean. The seasonal values are removed, and the remainder
smoothed to find the trend. The overall level is removed from the
seasonal component and added to the trend component. This process is
iterated a few times. The remainder component is the
residuals from the seasonal plus trend fit.
Several methods for the resulting class "stl" objects, see,
plot.stl.
R. B. Cleveland, W. S. Cleveland, J.E. McRae, and I. Terpenning (1990) STL: A Seasonal-Trend Decomposition Procedure Based on Loess. Journal of Official Statistics, 6, 3--73.
plot.stl for stl methods;
loess in package stats (which is not actually
used in stl).
StructTS for different kind of decomposition.
# NOT RUN {
require(graphics)
plot(stl(nottem, "per"))
plot(stl(nottem, s.window = 7, t.window = 50, t.jump = 1))
plot(stllc <- stl(log(co2), s.window = 21))
summary(stllc)
## linear trend, strict period.
plot(stl(log(co2), s.window = "per", t.window = 1000))
## Two STL plotted side by side :
stmd <- stl(mdeaths, s.window = "per") # non-robust
summary(stmR <- stl(mdeaths, s.window = "per", robust = TRUE))
op <- par(mar = c(0, 4, 0, 3), oma = c(5, 0, 4, 0), mfcol = c(4, 2))
plot(stmd, set.pars = NULL, labels = NULL,
main = "stl(mdeaths, s.w = \"per\", robust = FALSE / TRUE )")
plot(stmR, set.pars = NULL)
# mark the 'outliers' :
(iO <- which(stmR $ weights < 1e-8)) # 10 were considered outliers
sts <- stmR$time.series
points(time(sts)[iO], 0.8* sts[,"remainder"][iO], pch = 4, col = "red")
par(op) # reset
# }