R: Simulate from an ARIMA Model

arima.sim {stats} | R Documentation

## Simulate from an ARIMA Model

### Description

Simulate from an ARIMA model.

### Usage

    arima.sim(model, n, rand.gen = rnorm, innov = rand.gen(n, ...),
              n.start = NA, start.innov = rand.gen(n.start, ...),
              ...)

### Arguments

`model` | A list with component `ar` and/or `ma` giving the AR and MA coefficients respectively. Optionally a component `order` can be used. An empty list gives an ARIMA(0, 0, 0) model, that is white noise.
`n` | length of output series, before un-differencing. A strictly positive integer.
`rand.gen` | optional: a function to generate the innovations.
`innov` | an optional times series of innovations. If not provided, `rand.gen` is used.
`n.start` | length of ‘burn-in’ period. If `NA`, the default, a reasonable value is computed.
`start.innov` | an optional times series of innovations to be used for the burn-in period. If supplied there must be at least `n.start` values (and `n.start` is by default computed inside the function).
`...` | additional arguments for `rand.gen`. Most usefully, the standard deviation of the innovations generated by `rnorm` can be specified by `sd`.

### Details

See `arima` for the precise definition of an ARIMA model.

The ARMA model is checked for stationarity.

ARIMA models are specified via the `order` component of `model`, in the same way as for `arima`. Other aspects of the `order` component are ignored, but inconsistent specifications of the MA and AR orders are detected. The un-differencing assumes previous values of zero, and to remind the user of this, those values are returned.

Random inputs for the ‘burn-in’ period are generated by calling `rand.gen`.

### Value

A time-series object of class `"ts"`.

### See Also

`arima`

### Examples

    require(graphics)

    arima.sim(n = 63, list(ar = c(0.8897, -0.4858), ma = c(-0.2279, 0.2488)),
              sd = sqrt(0.1796))
    # mildly long-tailed
    arima.sim(n = 63, list(ar = c(0.8897, -0.4858), ma = c(-0.2279, 0.2488)),
              rand.gen = function(n, ...) sqrt(0.1796) * rt(n, df = 5))

    # An ARIMA simulation
    ts.sim <- arima.sim(list(order = c(1,1,0), ar = 0.7), n = 200)
    ts.plot(ts.sim)

[Package stats version 3.1.2 Index]