arch.univariate.volatility.VolatilityProcess.variance_bounds¶

VolatilityProcess.variance_bounds(resids: ndarray[Any, dtype[float64]], power: float = 2.0) → ndarray[Any, dtype[float64]][source]¶

Construct loose bounds for conditional variances.

These bounds are used in parameter estimation to ensure that the log-likelihood does not produce NaN values.

Parameters:¶

resids: ndarray[Any, dtype[float64]]¶

Approximate residuals to use to compute the lower and upper bounds on the conditional variance

power: float = 2.0¶

Power used in the model. 2.0, the default corresponds to standard ARCH models that evolve in squares.

Returns:¶

var_bounds – Array containing columns of lower and upper bounds with the same number of elements as resids

Return type:¶

numpy.ndarray