arch.univariate.SkewStudent

class arch.univariate.SkewStudent(random_state=None)[source]

Standardized Skewed Student’s distribution for use with ARCH models

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

name

The name of the distribution

random_state

The NumPy RandomState attached to the distribution