# forecast.Arima

From forecast v3.03
by Rob Hyndman

##### Forecasting using ARIMA or ARFIMA models

Returns forecasts and other information for univariate ARIMA models.

- Keywords
- ts

##### Usage

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

##### Arguments

- object
- An object of class "
`Arima`

", "`ar`

" or "`fracdiff`

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

,`auto.arima`

, - 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(50,99,by=1)`

. This is suitable for fan plots. - xreg
- Future values of an regression variables (for class
`Arima`

objects only). - lambda
- Box-Cox transformation parameter. Ignored if NULL. Otherwise, forecasts back-transformed via an inverse Box-Cox transformation.
- ...
- Other arguments.

##### 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).

##### 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)

##### 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`

.

##### Examples

```
fit <- Arima(WWWusage,c(3,1,0))
plot(forecast(fit))
x <- fracdiff.sim( 100, ma=-.4, d=.3)$series
fit <- arfima(x)
plot(forecast(fit,h=30))
```

*Documentation reproduced from package forecast, version 3.03, License: GPL (>= 2)*

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