R: Forecasting using ARIMA or ARFIMA models

forecast.fracdiff {forecast} | R Documentation

## Forecasting using ARIMA or ARFIMA models

### Description

Returns forecasts and other information for univariate ARIMA models.

### Usage

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

    ## 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,
      ...
    )

### 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`.

### 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 8.12 Index]