forecast.Arima: Forecasting using ARIMA or ARFIMA models

In forecast: Forecasting Functions for Time Series and Linear Models

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,
  simulate = FALSE,
  bootstrap = FALSE,
  innov = NULL,
  npaths = 5000,
  lambda = object$lambda,
  biasadj = attr(lambda, "biasadj"),
  ...
)

## S3 method for class 'Arima'
forecast(
  object,
  h = if (object$arma[5] > 1) 2 * object$arma[5] else 10,
  level = c(80, 95),
  fan = FALSE,
  xreg = NULL,
  simulate = FALSE,
  bootstrap = FALSE,
  innov = NULL,
  npaths = 5000,
  lambda = object$lambda,
  biasadj = attr(lambda, "biasadj"),
  ...
)

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

Arguments

object	An object of class Arima, ar or fracdiff. Usually the result of a call to stats::arima(), auto.arima(), stats::ar(), arfima() or fracdiff::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 levels for prediction intervals.
fan	If TRUE, level is set to seq(51, 99, by = 3). This is suitable for fan plots.
simulate	If TRUE, prediction intervals are produced by simulation rather than using analytic formulae. Errors are assumed to be normally distributed.
bootstrap	If TRUE, then prediction intervals are produced by simulation using resampled errors (rather than normally distributed errors). Ignored if innov is not NULL.
innov	Optional matrix of future innovations to be used in simulations. Ignored if simulate = FALSE. If provided, this overrides the bootstrap argument. The matrix should have h rows and npaths columns.
npaths	Number of sample paths used in computing simulated prediction intervals.
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 are ignored.
xreg	Future values of any regression variables. A numerical vector or matrix of external regressors; it should not be a data frame.

Details

For Arima or ar objects, the function calls stats::predict.Arima() or stats::predict.ar and constructs an object of class forecast from the results. For fracdiff objects, the calculations are all done within fracdiff::fracdiff() using the equations given by Peiris and Perera (1988).

Value

An object of class forecast.

forecast class

An object of class forecast is a list usually 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.

residuals

Residuals from the fitted model. For models with additive errors, the residuals will be x minus the fitted values.

fitted

Fitted values (one-step forecasts)

The function summary can be used to obtain and print a summary of the results, while the functions plot and autoplot produce plots of the forecasts and prediction intervals. The generic accessor functions fitted.values and residuals extract various useful features from the underlying model.

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

stats::predict.Arima(), stats::predict.ar(), auto.arima(), Arima(), stats::arima(), stats::ar(), arfima().

Examples

fit <- Arima(WWWusage, c(3, 1, 0))
plot(forecast(fit))

library(fracdiff)
x <- fracdiff.sim(100, ma = -0.4, d = 0.3)$series
fit <- arfima(x)
plot(forecast(fit, h = 30))

forecast documentation built on March 18, 2026, 9:07 a.m.