predict.Arima {stats} | R Documentation

## Forecast from ARIMA fits

### Description

Forecast from models fitted by `arima`.

### Usage

    ## S3 method for class 'Arima':
    predict(object, n.ahead = 1, newxreg = NULL,
            se.fit = TRUE, ...)

### Arguments

`object` | The result of an `arima` fit.
`n.ahead` | The number of steps ahead for which prediction is required.
`newxreg` | New values of `xreg` to be used for prediction. Must have at least `n.ahead` rows.
`se.fit` | Logical: should standard errors of prediction be returned?
`...` | arguments passed to or from other methods.

### Details

Finite-history prediction is used, via `KalmanForecast`. This is only statistically efficient if the MA part of the fit is invertible, so `predict.Arima` will give a warning for non-invertible MA models.

The standard errors of prediction exclude the uncertainty in the estimation of the ARMA model and the regression coefficients. According to Harvey (1993, pp. 58–9) the effect is small.

### Value

A time series of predictions, or if `se.fit = TRUE`, a list with components `pred`, the predictions, and `se`, the estimated standard errors. Both components are time series.

### References

Durbin, J. and Koopman, S. J. (2001) Time Series Analysis by State Space Methods. Oxford University Press.

Harvey, A. C. and McKenzie, C. R. (1982) Algorithm AS182. An algorithm for finite sample prediction from ARIMA processes. Applied Statistics 31, 180–187.

Harvey, A. C. (1993) Time Series Models, 2nd Edition, Harvester Wheatsheaf, sections 3.3 and 4.4.

### See Also

`arima`

### Examples

    data(lh)
    predict(arima(lh, order = c(3,0,0)), n.ahead = 12)

    data(USAccDeaths)
    (fit <- arima(USAccDeaths, order = c(0,1,1),
                  seasonal = list(order=c(0,1,1))))
    predict(fit, n.ahead = 6)

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