arch.univariate.SkewStudent¶

class arch.univariate.SkewStudent(random_state=None, *, seed=None)[source]¶

Standardized Skewed Student’s distribution for use with ARCH models

Parameters¶

random_state : RandomState, optional¶

Deprecated since version 5.0: random_state is deprecated. Use seed instead.

seed : {int, Generator, RandomState}, optional¶

Random number generator instance or int to use. Set to ensure reproducibility. If using an int, the argument is passed to np.random.default_rng. If not provided, default_rng is used with system-provided entropy.

Notes

The Standardized Skewed Student’s distribution (1) takes two parameters, \(\eta\) and \(\lambda\). \(\eta\) controls the tail shape and is similar to the shape parameter in a Standardized Student’s t. \(\lambda\) controls the skewness. When \(\lambda=0\) the distribution is identical to a standardized Student’s t.

References

1

Hansen, B. E. (1994). Autoregressive conditional density estimation. International Economic Review, 35(3), 705–730. <https://www.ssc.wisc.edu/~bhansen/papers/ier_94.pdf>

Methods

bounds(resids)	Parameter bounds for use in optimization.
cdf(resids[, parameters])	Cumulative distribution function
constraints()	Construct arrays to use in constrained optimization.
loglikelihood(parameters, resids, sigma2[, ...])	Computes the log-likelihood of assuming residuals are have a standardized (to have unit variance) Skew Student's t distribution, conditional on the variance.
moment(n[, parameters])	Moment of order n
parameter_names()	Names of distribution shape parameters
partial_moment(n[, z, parameters])	Order n lower partial moment from -inf to z
ppf(pits[, parameters])	Inverse cumulative density function (ICDF)
simulate(parameters)	Simulates i.i.d.
starting_values(std_resid)	Construct starting values for use in optimization.

Properties

generator	The NumPy Generator or RandomState attached to the distribution
name	The name of the distribution
random_state	The NumPy RandomState attached to the distribution