Returns forecasts and other information for univariate ARIMA models.

## Usage

```
# S3 method for fracdiff
forecast(
object,
h = 10,
level = c(80, 95),
fan = FALSE,
lambda = object$lambda,
biasadj = NULL,
...
)
# S3 method for Arima
forecast(
object,
h = ifelse(object$arma[5] > 1, 2 * object$arma[5], 10),
level = c(80, 95),
fan = FALSE,
xreg = NULL,
lambda = object$lambda,
bootstrap = FALSE,
npaths = 5000,
biasadj = NULL,
...
)
# S3 method for ar
forecast(
object,
h = 10,
level = c(80, 95),
fan = FALSE,
lambda = NULL,
bootstrap = FALSE,
npaths = 5000,
biasadj = FALSE,
...
)
```

## Arguments

- object
An object of class "

`Arima`

", "`ar`

" or "`fracdiff`

". Usually the result of a call to`arima`

,`auto.arima`

,`ar`

,`arfima`

or`fracdiff`

.- h
Number of periods for forecasting. If

`xreg`

is used,`h`

is ignored and the number of forecast periods is set to the number of rows of`xreg`

.- level
Confidence level 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.

- xreg
Future values of an regression variables (for class

`Arima`

objects only). A numerical vector or matrix of external regressors; it should not be a data frame.- bootstrap
If

`TRUE`

, then prediction intervals computed using simulation with resampled errors.- npaths
Number of sample paths used in computing simulated prediction intervals when

`bootstrap=TRUE`

.

## 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 `forecast.Arima`

.

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

For `Arima`

or `ar`

objects, the function calls
`predict.Arima`

or `predict.ar`

and
constructs an object of class "`forecast`

" from the results. For
`fracdiff`

objects, the calculations are all done within
`forecast.fracdiff`

using the equations given by Peiris and
Perera (1988).

## References

Peiris, M. & Perera, B. (1988), On prediction with fractionally
differenced ARIMA models, *Journal of Time Series Analysis*,
**9**(3), 215-220.

## See also

`predict.Arima`

,
`predict.ar`

, `auto.arima`

,
`Arima`

, `arima`

, `ar`

,
`arfima`

.