arch.univariate.base.ARCHModel.fit

ARCHModel.fit(update_freq=1, disp='final', starting_values=None, cov_type='robust', show_warning=True, first_obs=None, last_obs=None, tol=None, options=None, backcast=None)

Estimate model parameters

Parameters:

update_freqint, optional

Frequency of iteration updates. Output is generated every update_freq iterations. Set to 0 to disable iterative output.

disp{bool, “off”, “final”}

Either ‘final’ to print optimization result or ‘off’ to display nothing. If using a boolean, False is “off” and True is “final”

starting_valuesndarray, optional

Array of starting values to use. If not provided, starting values are constructed by the model components.

cov_typestr, 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_warningbool, 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

tolfloat, optional

Tolerance for termination.

optionsdict, optional

Options to pass to scipy.optimize.minimize. Valid entries include ‘ftol’, ‘eps’, ‘disp’, and ‘maxiter’.

backcast{float, ndarray}, 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.

Returns:

resultsARCHModelResult

Object containing model results

Notes

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

Parameters are optimized using SLSQP.

Return type:

ARCHModelResult