Forecasting using ARIMA or ARFIMA models

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 = if (object$arma[5] > 1) 2 * object$arma[5] else 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 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.
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.
bootstrap: If TRUE, then prediction intervals are produced by simulation using resampled errors (rather than normally distributed errors).
npaths: Number of sample paths used in computing simulated prediction intervals.

Value

An object of class forecast.

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).

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 accessors functions fitted.values and residuals extract various useful features from the underlying model.

References

Peiris, M. & Perera, B. (1988), On prediction with fractionally differenced ARIMA models, Journal of Time Series Analysis, 9(3), 215-220.

Author

Rob J Hyndman

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))