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>

Attributes
name

The name of the distribution

random_state

The NumPy RandomState attached to the distribution

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.

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