ARMAResult.simulate#

ARMAResult.simulate(n=200, *, seed=None, burn=_SIMULATION_BURN)[source]#

A fresh sample path at the fitted parameters.

The stationary ARMA part – seasonal and non-seasonal polynomials multiplied out – is generated from a zero start over burn + n periods with the first burn discarded; the deterministic block is added on the differenced scale with the time index running 1 .. n, exactly as the estimator laid it out; and the result is integrated d and D times from zero initial levels, so the first d + sD entries of the returned path are zero.

Parameters:

  • n (int) – Observations kept, on the level scale; must exceed d + sD.

  • seed (int | Generator | None) – Seed or generator.

  • burn (int) – Periods discarded from the start.

Return type:

NDArray[double]

Returns:

An array of shape (n,).

Raises:

SpecificationError – If the counts are not usable or the fit carries exogenous regressors, whose future the result cannot know.

Example

The simulated variance and mean are the ARMA(1, 1) closed forms at the estimates:

>>> rng = np.random.default_rng(0)
>>> e = rng.standard_normal(600)
>>> y = np.zeros(600)
>>> for t in range(1, 600):
...     y[t] = 0.6 * y[t - 1] + e[t] + 0.4 * e[t - 1]
>>> res = ARMA(y, order=(1, 1)).fit()
>>> path = res.simulate(50000, seed=0)
>>> phi, theta = float(res.ar_params[0]), float(res.ma_params[0])
>>> variance = res.sigma2 * (1 + 2 * phi * theta + theta**2) / (1 - phi**2)
>>> bool(abs(path.var() - variance) < 0.05), bool(abs(path.mean() - res.beta[0]) < 0.05)
(True, True)
>>> ARIMA(np.cumsum(y), order=(1, 1, 1)).fit().simulate(1)
Traceback (most recent call last):
    ...
cultivars.exceptions.SpecificationError: n must exceed the integration orders (1); ...
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