Returns forecasts and prediction intervals for a theta method forecast.

## Arguments

- y
a numeric vector or time series of class

`ts`

- h
Number of periods for forecasting

- 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`

".

The function `summary`

is used to obtain and print a summary of the
results, while the function `plot`

produces a plot of the forecasts and
prediction intervals.

The generic accessor functions `fitted.values`

and `residuals`

extract useful features of the value returned by `rwf`

.

An object of class `"forecast"`

is a list 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 (either

`object`

itself or the time series used to create the model stored as`object`

).- residuals
Residuals from the fitted model. That is x minus fitted values.

- fitted
Fitted values (one-step forecasts)

## 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.

## 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.

## Examples

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