arch.univariate.base.ARCHModel.fit

ARCHModel.fit(update_freq: int = 1, disp: 'off' | 'final' | bool = 'final', starting_values: ndarray[tuple[int], dtype[float64]] | 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: float | ndarray[tuple[int], dtype[float64]] | None = 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. Must not be negative.

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

Either ‘final’ to print optimization result or ‘off’ to display nothing. Not case sensitive. If using a boolean, False is “off” and True is “final”. The integers 0 and 1 are accepted as booleans.

starting_values: ndarray[tuple[int], dtype[float64]] | Series | None = None

Array of starting values to use. If not provided, starting values are constructed by the model components. Must have one finite element for each parameter of the model. Starting values that do not satisfy the constraints and bounds of the model are ignored, and a StartingValueWarning is issued.

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. Not case sensitive. Any other value raises a ValueError.

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. Dates, strings and periods can only be used with pandas inputs that have a DatetimeIndex or a PeriodIndex. An integer must be in [-nobs, nobs], and a date must be in the index. A negative integer counts from the end, as in a slice, so that first_obs=-100 uses the last 100 observations.

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

Last observation to use when estimating model. An integer must be in [-nobs, nobs], and a date must be in the index. As in a slice, the observation at last_obs is not used, and a negative integer counts from the end, so that last_obs=-1 drops the last observation.

tol: float | None = None

Tolerance for termination. Must not be negative.

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

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

backcast: float | ndarray[tuple[int], dtype[float64]] | None = 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. A float must be positive, and an array must contain finite values.

Returns:

results – Object containing model results.

Return type:

arch.univariate.base.ARCHModelResult

Raises:

  • RuntimeError – If the model was created without data.

  • TypeError – If an argument is not of the documented type, for example a float for update_freq or disp.

  • ValueError – If update_freq is negative, tol is negative or not finite, backcast is not positive and finite, starting_values does not have one finite element for each parameter, first_obs or last_obs is outside the sample, cov_type or disp is not one of the options (disp can also be an integer other than 0 and 1), or the model has more parameters than the number of observations used to estimate it.

Notes

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

Parameters are optimized using SLSQP.