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)
```

x

univariate time series to be decomposed.
This should be an object of class `"ts"`

with a frequency
greater than one.

s.window

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.

s.degree

degree of locally-fitted polynomial in seasonal extraction. Should be zero or one.

t.window

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.

t.degree

degree of locally-fitted polynomial in trend extraction. Should be zero or one.

l.window

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.

l.degree

degree of locally-fitted polynomial for the subseries low-pass filter. Must be 0 or 1.

s.jump, t.jump, l.jump

integers at least one to increase speed of
the respective smoother. Linear interpolation happens between every
`*.jump`

th value.

robust

logical indicating if robust fitting be used in the
`loess`

procedure.

inner

integer; the number of ‘inner’ (backfitting) iterations; usually very few (2) iterations suffice.

outer

integer; the number of ‘outer’ robustness iterations.

na.action

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 **i**nner iterations

number of **o**uter 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 # }