, disp='final', starting_values=None, cov_type='robust', show_warning=True, first_obs=None, last_obs=None, tol=None, options=None, backcast=None)

Fits the model given a nobs by 1 vector of sigma2 values

  • update_freq (int, optional) – Frequency of iteration updates. Output is generated every update_freq iterations. Set to 0 to disable iterative output.

  • disp (str) – Either ‘final’ to print optimization result or ‘off’ to display nothing

  • starting_values (ndarray, optional) – Array of starting values to use. If not provided, starting values are constructed by the model components.

  • cov_type (str, optional) – Estimation method of parameter covariance. Supported options are ‘robust’, which does not assume the Information Matrix Equality holds and ‘classic’ which does. In the ARCH literature, ‘robust’ corresponds to Bollerslev-Wooldridge covariance estimator.

  • show_warning (bool, optional) – Flag indicating whether convergence warnings should be shown.

  • first_obs ({int, str, datetime, Timestamp}) – First observation to use when estimating model

  • last_obs ({int, str, datetime, Timestamp}) – Last observation to use when estimating model

  • tol (float, optional) – Tolerance for termination.

  • options (dict, optional) – Options to pass to scipy.optimize.minimize. Valid entries include ‘ftol’, ‘eps’, ‘disp’, and ‘maxiter’.

  • backcast (float, optional) – Value to use as backcast. Should be measure \(\sigma^2_0\) since model-specific non-linear transformations are applied to value before computing the variance recursions.


results – Object containing model results

Return type



A ConvergenceWarning is raised if SciPy’s optimizer indicates difficulty finding the optimum.

Parameters are optimized using SLSQP.