# forecast.Arima

From forecast v7.1
by Rob Hyndman

##### Forecasting using ARIMA or ARFIMA models

Returns forecasts and other information for univariate ARIMA models.

- Keywords
- ts

##### Usage

```
"forecast"(object, h=ifelse(object$arma[5]>1,2*object$arma[5],10), level=c(80,95), fan=FALSE, xreg=NULL, lambda=object$lambda, bootstrap=FALSE, npaths=5000, biasadj=FALSE, ...)
"forecast"(object, h=10, level=c(80,95), fan=FALSE, lambda=NULL, bootstrap=FALSE, npaths=5000, biasadj=FALSE, ...)
"forecast"(object, h=10, level=c(80,95), fan=FALSE, lambda=object$lambda, 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. - 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.
- biasadj
- Use adjusted back-transformed mean for Box-Cox transformations. If TRUE, point forecasts and fitted values are mean forecast. Otherwise, these points can be considered the median of the forecast densities.
- 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`

. - ...
- 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

- 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)

`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:
##### 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

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

*Documentation reproduced from package forecast, version 7.1, License: GPL (>= 2)*

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