forecast.stl: Forecasting using stl objects
In forecast: Forecasting Functions for Time Series and Linear Models

forecast.stl

R Documentation

Forecasting using stl objects

Description

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 = FALSE,
  xreg = NULL,
  newxreg = NULL,
  allow.multiplicative.trend = FALSE,
  ...
)

## S3 method for class 'stlm'
forecast(
  object,
  h = 2 * object$m,
  level = c(80, 95),
  fan = FALSE,
  lambda = object$lambda,
  biasadj = attr(lambda, "biasadj"),
  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 `stats::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. If `xreg` is used, `h` is ignored and the number of forecast periods is set to the number of rows of `xreg`.
`level`	Confidence levels 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 numeric vector or univariate time series of class `ts`
`s.window`	Either the character string `"periodic"` or the span (in lags) of the loess window for seasonal extraction.
`t.window`	A number to control the smoothness of the trend. See `stats::stl()` for details.
`robust`	If `TRUE`, robust fitting will be used in the loess procedure within `stats::stl()`.
`x`	Deprecated. Included for backwards compatibility.

Details

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 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.

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.

Author(s)

Rob J Hyndman

Examples


tsmod <- stlm(USAccDeaths, modelfunction = ar)
plot(forecast(tsmod, h = 36))

decomp <- stl(USAccDeaths, s.window = "periodic")
plot(forecast(decomp))

plot(stlf(AirPassengers, lambda = 0))

forecast documentation built on March 18, 2026, 9:07 a.m.