R: Forecasting using ARIMA or ARFIMA models

forecast.Arima {forecast} | R Documentation

## Forecasting using ARIMA or ARFIMA models

### Description

Returns forecasts and other information for univariate ARIMA models.

### 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$lambda,
        bootstrap=FALSE, npaths=5000, biasadj=NULL, ...)
    ## S3 method for class 'ar'
    forecast(object, h=10, level=c(80,95), fan=FALSE, lambda=NULL,
        bootstrap=FALSE, npaths=5000, biasadj=FALSE, ...)
    ## S3 method for class 'fracdiff'
    forecast(object, h=10, level=c(80,95), fan=FALSE,
        lambda=object$lambda, biasadj=NULL, ...)

### 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. By default, the value is taken from what was used when fitting the model.
`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

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)

### Author(s)

Rob J Hyndman

### 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))

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

[Package forecast version 8.0 Index]