arch.univariate.base.ARCHModel.fit¶

ARCHModel.fit(update_freq: int = 1, disp: bool | 'off' | 'final' = 'final', starting_values: ndarray | Series | None = None, cov_type: 'robust' | 'classic' = 'robust', show_warning: bool = True, first_obs: int | str | datetime | datetime64 | Timestamp | None = None, last_obs: int | str | datetime | datetime64 | Timestamp | None = None, tol: float | None = None, options: dict[str, Any] | None = None, backcast: None | float | ndarray = None) → ARCHModelResult[source]¶

Estimate model parameters

Parameters:¶

update_freq: int = 1¶

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

disp: bool | 'off' | 'final' = 'final'¶

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

starting_values: ndarray | Series | None = None¶

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

cov_type: 'robust' | 'classic' = 'robust'¶

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 = True¶

Flag indicating whether convergence warnings should be shown.

first_obs: int | str | datetime | datetime64 | Timestamp | None = None¶

First observation to use when estimating model

last_obs: int | str | datetime | datetime64 | Timestamp | None = None¶

Last observation to use when estimating model

tol: float | None = None¶

Tolerance for termination.

options: dict[str, Any] | None = None¶

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

backcast: None | float | ndarray = None¶

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:¶

results – Object containing model results

Return type:¶

ARCHModelResult

Notes

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

Parameters are optimized using SLSQP.