Forecasts of STL objects are obtained by applying a non-seasonal forecasting method to the seasonally adjusted data and re-seasonalizing using the last year of the seasonal component.

## Usage

```
# S3 method for class 'stl'
forecast(
object,
method = c("ets", "arima", "naive", "rwdrift"),
etsmodel = "ZZN",
forecastfunction = NULL,
h = frequency(object$time.series) * 2,
level = c(80, 95),
fan = FALSE,
lambda = NULL,
biasadj = NULL,
xreg = NULL,
newxreg = NULL,
allow.multiplicative.trend = FALSE,
...
)
stlm(
y,
s.window = 7 + 4 * seq(6),
robust = FALSE,
method = c("ets", "arima"),
modelfunction = NULL,
model = NULL,
etsmodel = "ZZN",
lambda = NULL,
biasadj = FALSE,
xreg = NULL,
allow.multiplicative.trend = FALSE,
x = y,
...
)
# S3 method for class 'stlm'
forecast(
object,
h = 2 * object$m,
level = c(80, 95),
fan = FALSE,
lambda = object$lambda,
biasadj = NULL,
newxreg = NULL,
allow.multiplicative.trend = FALSE,
...
)
stlf(
y,
h = frequency(x) * 2,
s.window = 7 + 4 * seq(6),
t.window = NULL,
robust = FALSE,
lambda = NULL,
biasadj = FALSE,
x = y,
...
)
```

## Arguments

- object
An object of class

`stl`

or`stlm`

. Usually the result of a call to`stl`

or`stlm`

.- method
Method to use for forecasting the seasonally adjusted series.

- etsmodel
The ets model specification passed to

`ets`

. By default it allows any non-seasonal model. If`method!="ets"`

, this argument is ignored.- forecastfunction
An alternative way of specifying the function for forecasting the seasonally adjusted series. If

`forecastfunction`

is not`NULL`

, then`method`

is ignored. Otherwise`method`

is used to specify the forecasting method to be used.- h
Number of periods for forecasting.

- level
Confidence level for prediction intervals.

- fan
If

`TRUE`

, level is set to seq(51,99,by=3). This is suitable for fan plots.- lambda
Box-Cox transformation parameter. If

`lambda="auto"`

, then a transformation is automatically selected using`BoxCox.lambda`

. The transformation is ignored if NULL. Otherwise, data transformed before model is estimated.- biasadj
Use adjusted back-transformed mean for Box-Cox transformations. If transformed data is used to produce forecasts and fitted values, a regular back transformation will result in median forecasts. If biasadj is TRUE, an adjustment will be made to produce mean forecasts and fitted values.

- xreg
Historical regressors to be used in

`auto.arima()`

when`method=="arima"`

.- newxreg
Future regressors to be used in

`forecast.Arima()`

.- allow.multiplicative.trend
If TRUE, then ETS models with multiplicative trends are allowed. Otherwise, only additive or no trend ETS models are permitted.

- ...
Other arguments passed to

`forecast.stl`

,`modelfunction`

or`forecastfunction`

.- y
A univariate numeric time series of class

`ts`

- s.window
Either the character string “periodic” or the span (in lags) of the loess window for seasonal extraction.

- robust
If

`TRUE`

, robust fitting will used in the loess procedure within`stl`

.- modelfunction
An alternative way of specifying the function for modelling the seasonally adjusted series. If

`modelfunction`

is not`NULL`

, then`method`

is ignored. Otherwise`method`

is used to specify the time series model to be used.- model
Output from a previous call to

`stlm`

. If a`stlm`

model is passed, this same model is fitted to y without re-estimating any parameters.- x
Deprecated. Included for backwards compatibility.

- t.window
A number to control the smoothness of the trend. See

`stl`

for details.

## Value

`stlm`

returns an object of class `stlm`

. The other
functions return objects of class `forecast`

.

There are many methods for working with `forecast`

objects
including `summary`

to obtain and print a summary of the results, while
`plot`

produces a plot of the forecasts and prediction intervals. The
generic accessor functions `fitted.values`

and `residuals`

extract
useful features.

## Details

`stlm`

takes a time series `y`

, applies an STL decomposition, and
models the seasonally adjusted data using the model passed as
`modelfunction`

or specified using `method`

. It returns an object
that includes the original STL decomposition and a time series model fitted
to the seasonally adjusted data. This object can be passed to the
`forecast.stlm`

for forecasting.

`forecast.stlm`

forecasts the seasonally adjusted data, then
re-seasonalizes the results by adding back the last year of the estimated
seasonal component.

`stlf`

combines `stlm`

and `forecast.stlm`

. It takes a
`ts`

argument, applies an STL decomposition, models the seasonally
adjusted data, reseasonalizes, and returns the forecasts. However, it allows
more general forecasting methods to be specified via
`forecastfunction`

.

`forecast.stl`

is similar to `stlf`

except that it takes the STL
decomposition as the first argument, instead of the time series.

Note that the prediction intervals ignore the uncertainty associated with the seasonal component. They are computed using the prediction intervals from the seasonally adjusted series, which are then reseasonalized using the last year of the seasonal component. The uncertainty in the seasonal component is ignored.

The time series model for the seasonally adjusted data can be specified in
`stlm`

using either `method`

or `modelfunction`

. The
`method`

argument provides a shorthand way of specifying
`modelfunction`

for a few special cases. More generally,
`modelfunction`

can be any function with first argument a `ts`

object, that returns an object that can be passed to `forecast`

.
For example, `forecastfunction=ar`

uses the `ar`

function
for modelling the seasonally adjusted series.

The forecasting method for the seasonally adjusted data can be specified in
`stlf`

and `forecast.stl`

using either `method`

or
`forecastfunction`

. The `method`

argument provides a shorthand way
of specifying `forecastfunction`

for a few special cases. More
generally, `forecastfunction`

can be any function with first argument a
`ts`

object, and other `h`

and `level`

, which returns an
object of class `forecast`

. For example,
`forecastfunction=thetaf`

uses the `thetaf`

function for
forecasting the seasonally adjusted series.