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CLN: Backport documentation fixes
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Backport documentation fixes from variance forecasting
Change flake8 to 100 characters
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@bashtage
bashtage committed Dec 14, 2016
1 parent 86fe3ff commit e422111
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Showing 2 changed files with 58 additions and 53 deletions.
106 changes: 54 additions & 52 deletions arch/univariate/distribution.py
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Expand Up @@ -29,19 +29,19 @@ def __init__(self, name):
self.num_params = 0
self._parameters = None

def _simulator(self, nobs):
def _simulator(self, size):
"""
Simulate i.i.d. draws from the distribution
Parameters
----------
nobs: int
Number of draws from the distribution
size : int or tuple
Shape of the draws from the distribution
Returns
-------
rvs : 1-d array
Simulated pseudo random normal variables
Simulated pseudo random variables
Notes
-----
Expand All @@ -62,7 +62,7 @@ def simulate(self, parameters):
Returns
-------
simulator : callable
Callable that take a single, integer argument and returns i.i.d.
Callable that take a single output size argument and returns i.i.d.
draws from the distribution
"""
raise NotImplementedError(
Expand Down Expand Up @@ -104,7 +104,7 @@ def loglikelihoood(self, parameters, resids, sigma2, individual=False):
Parameters
----------
parameters : 1-d array
Distribution parameters
Distribution shape parameters
resids : 1-d array
nobs array of model residuals
sigma2 : 1-d array
Expand All @@ -123,7 +123,20 @@ def loglikelihoood(self, parameters, resids, sigma2, individual=False):

def starting_values(self, std_resid):
"""
Compute starting values from standardized residuals
Parameters
----------
std_resid : 1-d array
Estimated standardized residuals to use in computing starting
values for the shape parameter
Returns
-------
sv : 1-d array
The estimated shape parameters for the distribution
Notes
-----
Size of sv depends on the distribution
"""
raise NotImplementedError(
'Subclasses must implement') # pragma: no cover
Expand Down Expand Up @@ -166,7 +179,7 @@ def bounds(self, resids):
return tuple([])

def loglikelihoood(self, parameters, resids, sigma2, individual=False):
"""Computes the log-likelihood of assuming residuals are normally
r"""Computes the log-likelihood of assuming residuals are normally
distributed, conditional on the variance
Parameters
Expand All @@ -192,8 +205,8 @@ def loglikelihoood(self, parameters, resids, sigma2, individual=False):
.. math::
\\ln f\\left(x\\right)=-\\frac{1}{2}\\ln2\\pi\\sigma^{2}
-\\frac{x^{2}}{2\\sigma^{2}}
\ln f\left(x\right)=-\frac{1}{2}\left(\ln2\pi+\ln\sigma^{2}
+\frac{x^{2}}{\sigma^{2}}\right)
"""
lls = -0.5 * (log(2 * pi) + log(sigma2) + resids ** 2.0 / sigma2)
Expand All @@ -203,19 +216,6 @@ def loglikelihoood(self, parameters, resids, sigma2, individual=False):
return sum(lls)

def starting_values(self, std_resid):
"""
Parameters
----------
std_resid : 1-d array
Estimated standardized residuals to use in computing starting
values for the shape parameter
Returns
-------
sv : empty array
The normal distribution has no shape parameters
"""
return empty(0)

def _simulator(self, nobs):
Expand All @@ -234,9 +234,8 @@ class StudentsT(Distribution):
"""

def __init__(self):
super(StudentsT, self).__init__('Normal')
super(StudentsT, self).__init__('Standardized Student\'s t')
self.num_params = 1
self.name = 'Standardized Student\'s t'

def constraints(self):
return array([[1], [-1]]), array([2.05, -500.0])
Expand All @@ -245,7 +244,7 @@ def bounds(self, resids):
return [(2.05, 500.0)]

def loglikelihoood(self, parameters, resids, sigma2, individual=False):
"""Computes the log-likelihood of assuming residuals are have a
r"""Computes the log-likelihood of assuming residuals are have a
standardized (to have unit variance) Student's t distribution,
conditional on the variance.
Expand All @@ -272,10 +271,10 @@ def loglikelihoood(self, parameters, resids, sigma2, individual=False):
.. math::
\\ln\\Gamma\\left(\\frac{\\nu+1}{2}\\right)
-\\ln\\Gamma\\left(\\frac{\\nu}{2}\\right)
-\\frac{1}{2}\\ln(\\pi\\left(\\nu-2\\right)\\sigma^{2})
-\\frac{\\nu+1}{2}\\ln(1+x^{2}/(\\sigma^{2}(\\nu-2)))
\ln\Gamma\left(\frac{\nu+1}{2}\right)
-\ln\Gamma\left(\frac{\nu}{2}\right)
-\frac{1}{2}\ln(\pi\left(\nu-2\right)\sigma^{2})
-\frac{\nu+1}{2}\ln(1+x^{2}/(\sigma^{2}(\nu-2)))
where :math:`\Gamma` is the gamma function.
"""
Expand Down Expand Up @@ -312,10 +311,10 @@ def starting_values(self, std_resid):
sv = max((4.0 * k - 6.0) / (k - 3.0) if k > 3.75 else 12.0, 4.0)
return array([sv])

def _simulator(self, nobs):
def _simulator(self, size):
parameters = self._parameters
std_dev = sqrt(parameters[0] / (parameters[0] - 2))
return standard_t(self._parameters[0], nobs) / std_dev
return standard_t(self._parameters[0], size=size) / std_dev

def simulate(self, parameters):
parameters = asarray(parameters)[None]
Expand All @@ -329,12 +328,16 @@ def parameter_names(self):


class SkewStudent(Distribution):
"""
r"""
Standardized Skewed Student's [1]_ distribution for use with ARCH models
Notes
-----
For :math:`\\lambda=0` the distribution is standardized Student's t.
The Standardized Skewed Student's distribution takes two parameters,
:math:`\eta` and :math:`\lambda`. :math:`\eta` controls the tail shape
and is similar to the shape parameter in a Standardized Student's t.
:math:`\lambda` controls the skewness. When :math:`\lambda=0` the
distribution is identical to a standardized Student's t.
References
----------
Expand All @@ -346,9 +349,8 @@ class SkewStudent(Distribution):
"""

def __init__(self):
super(SkewStudent, self).__init__('Normal')
super(SkewStudent, self).__init__('Standardized Skew Student\'s t')
self.num_params = 2
self.name = 'Standardized Skew Student\'s t'

def constraints(self):
return array([[1, 0], [-1, 0], [0, 1], [0, -1]]), \
Expand All @@ -358,7 +360,7 @@ def bounds(self, resids):
return [(2.05, 300.0), (-1, 1)]

def loglikelihoood(self, parameters, resids, sigma2, individual=False):
"""Computes the log-likelihood of assuming residuals are have a
r"""Computes the log-likelihood of assuming residuals are have a
standardized (to have unit variance) Skew Student's t distribution,
conditional on the variance.
Expand All @@ -385,24 +387,23 @@ def loglikelihoood(self, parameters, resids, sigma2, individual=False):
.. math::
\\ln\\left[\\frac{bc}{\\sigma}\\left(1+\\frac{1}{\\eta-2}
\\left(\\frac{a+bx/\\sigma}
{1+sgn(x/\\sigma+a/b)\\lambda}\\right)^{2}\\right)
^{-\\left(\\eta+1\\right)/2}\\right],
\ln\left[\frac{bc}{\sigma}\left(1+\frac{1}{\eta-2}
\left(\frac{a+bx/\sigma}
{1+sgn(x/\sigma+a/b)\lambda}\right)^{2}\right)
^{-\left(\eta+1\right)/2}\right],
where :math:`2<\eta<\infty`, and :math:`-1<\lambda<1`.
The constants :math:`a`, :math:`b`, and :math:`c` are given by
.. math::
a=4\\lambda c\\frac{\\eta-2}{\\eta-1},
\\quad b^{2}=1+3\\lambda^{2}-a^{2},
\\quad c=\\frac{\\Gamma\\left(\\frac{\\eta+1}{2}\\right)}
{\\sqrt{\\pi\\left(\\eta-2\\right)}
\\Gamma\\left(\\frac{\\eta}{2}\\right)},
a=4\lambda c\frac{\eta-2}{\eta-1},
\quad b^{2}=1+3\lambda^{2}-a^{2},
\quad c=\frac{\Gamma\left(\frac{\eta+1}{2}\right)}
{\sqrt{\pi\left(\eta-2\right)}
\Gamma\left(\frac{\eta}{2}\right)},
and :math:`\Gamma` is the gamma function.
"""
eta, lam = parameters

Expand Down Expand Up @@ -470,7 +471,8 @@ def __const_a(self, parameters):
Returns
-------
float
a: float
Constant used in the distribution
"""
eta, lam = parameters
Expand All @@ -487,8 +489,8 @@ def __const_b(self, parameters):
Returns
-------
float
b: float
Constant used in the distribution
"""
eta, lam = parameters
a = self.__const_a(parameters)
Expand All @@ -504,8 +506,8 @@ def __const_c(self, parameters):
Returns
-------
float
c : float
Log of the constant used in loglikelihood
"""
eta, lam = parameters
# return gamma((eta+1)/2) / ((pi*(eta-2))**.5 * gamma(eta/2))
Expand Down
5 changes: 4 additions & 1 deletion setup.cfg
View file
@@ -1,2 +1,5 @@
[metadata]
description-file = README.md
description-file = README.md

[flake8]
max-line-length = 100

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