Theta method forecast

Returns forecasts and prediction intervals for a theta method forecast.

Usage

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

Arguments

y

a numeric vector or univariate time series of class ts

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.

x

Deprecated. Included for backwards compatibility.

Value

An object of class forecast.

Details

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 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.

See also

stats::arima(), meanf(), rwf(), ses()

Author

Rob J Hyndman

Examples

nile.fcast <- thetaf(Nile)
plot(nile.fcast)