class pymc.GARCH11(*args, steps=None, **kwargs)[source]#

GARCH(1,1) with Normal innovations. The model is specified by

\[y_t \sim N(0, \sigma_t^2)\]
\[\sigma_t^2 = \omega + \alpha_1 * y_{t-1}^2 + \beta_1 * \sigma_{t-1}^2\]

where sigma_t^2 (the error variance) follows a ARMA(1, 1) model.

omegatensor_like of float

omega > 0, mean variance

alpha_1tensor_like of float

alpha_1 >= 0, autoregressive term coefficient

beta_1tensor_like of float

beta_1 >= 0, alpha_1 + beta_1 < 1, moving average term coefficient

initial_voltensor_like of float

initial_vol >= 0, initial volatility, sigma_0


GARCH11.dist(omega, alpha_1, beta_1, ...[, ...])

Creates a tensor variable corresponding to the cls distribution.