# forecast.stl

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##### Forecasting using stl objects

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.

Keywords
ts
##### Usage
stlm(y, s.window=7, robust=FALSE, method=c("ets","arima"),  modelfunction=NULL, etsmodel="ZZN", lambda=NULL, xreg=NULL,  allow.multiplicative.trend=FALSE, x=y, ...)
stlf(y, h=frequency(x)*2, s.window=7, t.window=NULL, robust=FALSE, lambda=NULL, biasadj=FALSE, x=y, ...)
"forecast"(object, h = 2*object$m, level = c(80, 95), fan = FALSE, lambda=object$lambda, biasadj=FALSE, newxreg=NULL, allow.multiplicative.trend=FALSE, ...)
"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, ...)
##### Arguments
y
A univariate numeric time series of class ts
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.
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.
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.
etsmodel
The ets model specification passed to ets. By default it allows any non-seasonal model. If method!="ets", this argument is ignored.
xreg
Historical regressors to be used in auto.arima() when method=="arima".
newxreg
Future regressors to be used in forecast.Arima().
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. Ignored if NULL. Otherwise, data transformed before decomposition and back-transformed after forecasts are computed.
Use adjusted back-transformed mean for Box-Cox transformations. If TRUE, point forecasts and fitted values are mean forecast. Otherwise, these points can be considered the median of the forecast densities.
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 stl for details.
robust
If TRUE, robust fitting will used in the loess procedure within stl.
allow.multiplicative.trend
If TRUE, then ETS models with multiplicative trends are allowed. Otherwise, only additive or no trend ETS models are permitted.
x
Deprecated. Included for backwards compatibility.
...
Other arguments passed to forecast.stl, modelfunction or forecastfunction.
##### 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.

##### Value

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.

stl, forecast.ets, forecast.Arima.

##### Aliases
• forecast.stl
• stlf
• stl
• stlm
• forecast.stlm
##### Examples
tsmod <- stlm(USAccDeaths, modelfunction=ar)
plot(forecast(tsmod, h=36))

plot(stlf(AirPassengers, lambda=0))

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


Documentation reproduced from package forecast, version 7.2, License: GPL (>= 2)

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