mojolearn.GARCH#

class mojolearn.GARCH(p=1, o=0, q=1, mean='Constant', dist='normal', power=2.0, numeric_mode=None)[source]#

Bases: object

GARCH(p, o, q) conditional volatility model with normal errors.

Fits a constant- or zero-mean GARCH model by Gaussian maximum likelihood, following the arch package’s arch_model(y, mean='Constant'|'Zero', vol='GARCH', p=p, o=o, q=q, dist='normal'): arch’s variance recursion, backcast, variance bounds and starting values. o > 0 adds asymmetric (GJR) terms. fit takes one series of shape (n_obs,) or a batch of shape (batch_size, n_obs).

Parameters:

  • p (int, default 1) – Order of the lagged squared innovations (ARCH terms).

  • o (int, default 0) – Order of the asymmetric innovations; needs p > 0.

  • q (int, default 1) – Order of the lagged conditional variance (GARCH terms).

  • mean ({“Constant”, “Zero”}, default “Constant”) – Mean model. Other arch mean models (AR, HAR, LS) raise NotImplementedError.

  • dist ({“normal”}, default “normal”) – Error distribution; only "normal" is supported.

  • power (float, default 2.0) – Only 2.0 is supported (TARCH/APARCH powers raise NotImplementedError).

  • numeric_mode (str or None, default None) – Numeric mode for this model ('identical', 'deterministic' or 'fast'); None uses the process default (see mojolearn.set_numeric_mode()).

Variables:

  • params_ (ndarray of shape (2 + p + o + q,) or (batch_size, 2 + p + o + q), float32) – mu, omega, alpha[1..p], gamma[1..o], beta[1..q].

  • loglikelihood_ (float32 or ndarray of shape (batch_size,)) – Maximized Gaussian log-likelihood.

  • n_iter_ (int64 or ndarray of shape (batch_size,)) – Nelder-Mead iterations used.

  • conditional_volatility_ (ndarray of shape (n_obs,) or (batch_size, n_obs), float32) – Fitted conditional volatility.

Raises:

ValueError – If p, o or q is negative, all are zero, or o > 0 with p == 0.

Notes

Input must be float32; float64 raises TypeError. Rescaling is not supported: scale the data yourself if needed.

Examples

>>> import numpy as np, mojolearn
>>> r = np.random.default_rng(0).standard_normal(500).astype(np.float32)
>>> model = mojolearn.GARCH(p=1, q=1).fit(r)
>>> model.forecast(5).shape
(5,)
__init__(p=1, o=0, q=1, mean='Constant', dist='normal', power=2.0, numeric_mode=None)[source]#

Methods

fit(y[, horizon])

Fit the model to one series or a batch of series.

forecast([horizon])

Analytic conditional variance forecasts.
fit(y, horizon=1)[source]#

Fit the model to one series or a batch of series.

Parameters:

  • y (array-like of shape (n_obs,) or (batch_size, n_obs)) – Returns (or other zero-centered data), float32, finite, at least 10 observations per series.

  • horizon (int, default 1) – Variance forecast horizon computed alongside the fit (at least 1).

Returns:

self

Raises:

  • TypeError – If y is float64.

  • ValueError – If a series has fewer than 10 observations or y holds a non-finite value.

forecast(horizon=1)[source]#

Analytic conditional variance forecasts.

Parameters:

horizon (int, default 1) – Number of steps ahead. A horizon longer than the one computed at fit refits the stored series.

Returns:

ndarray of shape (horizon,) or (batch_size, horizon), float32 – Forecast conditional variances.