Returns forecasts and prediction intervals for a theta method forecast.
thetaf( y, h = ifelse(frequency(y) > 1, 2 * frequency(y), 10), level = c(80, 95), fan = FALSE, x = y )
a numeric vector or time series of class
Number of periods for forecasting
Confidence levels for prediction intervals.
If TRUE, level is set to seq(51,99,by=3). This is suitable for fan plots.
Deprecated. Included for backwards compatibility.
An object of class "
summary is used to obtain and print a summary of the
results, while the function
plot produces a plot of the forecasts and
The generic accessor functions
extract useful features of the value returned by
An object of class
"forecast" is a list containing at least the
A list containing information about the fitted model
The name of the forecasting method as a character string
Point forecasts as a time series
Lower limits for prediction intervals
Upper limits for prediction intervals
The confidence values associated with the prediction intervals
The original time series
object itself or the time series used to create the model
Residuals from the fitted model. That is x minus fitted values.
Fitted values (one-step forecasts)
The theta method of Assimakopoulos and Nikolopoulos (2000) is equivalent to simple exponential smoothing with drift. This is demonstrated in 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.
More general theta methods are available in the
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.
Rob J Hyndman
nile.fcast <- thetaf(Nile) plot(nile.fcast)