Forecasting model using STL with a generative time series model

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

Usage

stlm(
  y,
  s.window = 7 + 4 * seq(6),
  t.window = NULL,
  robust = FALSE,
  method = c("ets", "arima"),
  modelfunction = NULL,
  model = NULL,
  etsmodel = "ZZN",
  lambda = NULL,
  biasadj = FALSE,
  xreg = NULL,
  allow.multiplicative.trend = FALSE,
  x = y,
  ...
)

Arguments

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 used in the loess procedure within stats::stl().
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.
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.
etsmodel: The ets model specification passed to ets(). By default it allows any non-seasonal model. If method != "ets", this argument is ignored.
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".
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 modelfunction.

Value

An object of class stlm.

Details

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, modelfunction = ar uses the ar() function for modelling the seasonally adjusted series.

Author

Rob J Hyndman

Examples


tsmod <- stlm(USAccDeaths, modelfunction = ar)
forecast(tsmod, h = 36) |> autoplot()


decomp <- stl(USAccDeaths, s.window = "periodic")
forecast(decomp) |> autoplot()