Theta method forecasts.

Returns forecasts and prediction intervals for a theta method forecast. thetaf() is a convenience function that combines theta_model() and forecast.theta_model(). The theta method of Assimakopoulos and Nikolopoulos (2000) is equivalent to simple exponential smoothing with drift (Hyndman and Billah, 2003). The series is tested for seasonality using the test outlined in A&N. If deemed seasonal, the series is seasonally adjusted using a classical multiplicative decomposition before applying the theta method. The resulting forecasts are then reseasonalized. Prediction intervals are computed using the underlying state space model.

Usage

# S3 method for class 'theta_model'
forecast(
  object,
  h = if (frequency(object$y) > 1) 2 * frequency(object$y) else 10,
  level = c(80, 95),
  fan = FALSE,
  lambda = object$lambda,
  biasadj = FALSE,
  ...
)

thetaf(
  y,
  h = if (frequency(y) > 1) 2 * frequency(y) else 10,
  level = c(80, 95),
  fan = FALSE,
  lambda = NULL,
  biasadj = FALSE,
  x = y,
  ...
)

Arguments

object: An object of class theta_model created by theta_model().
h: Number of periods for forecasting. Default value is twice the largest seasonal period (for seasonal data) or ten (for non-seasonal data).
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.
...: Other arguments passed to forecast.ets.
y: a numeric vector or univariate time series of class ts
x: Deprecated. Included for backwards compatibility.

Value

An object of class forecast.

Details

More general theta methods are available in the forecTheta package.

forecast class

An object of class forecast is a list usually containing at least the following elements:

model: A list containing information about the fitted model
method: The name of the forecasting method as a character string
mean: Point forecasts as a time series
lower: Lower limits for prediction intervals
upper: Upper limits for prediction intervals
level: The confidence values associated with the prediction intervals
x: The original time series.
residuals: Residuals from the fitted model. For models with additive errors, the residuals will be x minus the fitted values.
fitted: Fitted values (one-step forecasts)

The function summary can be used to obtain and print a summary of the results, while the functions plot and autoplot produce plots of the forecasts and prediction intervals. The generic accessors functions fitted.values and residuals extract various useful features from the underlying model.

References

Assimakopoulos, V. and Nikolopoulos, K. (2000). The theta model: a decomposition approach to forecasting. International Journal of Forecasting 16, 521-530.

Hyndman, R.J., and Billah, B. (2003) Unmasking the Theta method. International J. Forecasting, 19, 287-290.

Author

Rob J Hyndman

Examples

nile_fit <- theta_model(Nile)
forecast(nile_fit) |> autoplot()