How can I set nu=4.0 in this situation?
model = arch_model(data)
from arch.univariate import StudentsT
model.distribution = StudentsT()
How can I set nu=4.0 in this situation?
model = arch_model(data)
from arch.univariate import StudentsT
model.distribution = StudentsT()
If you want to pass a specific degree of freedom to the function StudentsT, use the method _ord_t_partial_moment:
StudentsT._ord_t_partial_moment(n, z, nu)
Found in: arch univariate distribution
@staticmethod
def _ord_t_partial_moment(n: int, z: float, nu: float) -> float:
r"""
Partial moment calculation for ordinary parameterization of Students t with degrees of freedom=nu
Parameters
----------
n : int
Order of the partial moment
z : float
Upper limit for the partial moment integral
nu : float
Degrees of freedom
Returns
-------
float
Calculated moment
References
----------
.. [1] Winkler et al. (1972) "The Determination of Partial Moments"
*Management Science* Vol. 19 No. 3
Notes
-----
The lower partial moment of order n for variable x up to z is defined by:
.. math::
\int_{-\infty}^{z}x^{n}f(x)dx
For more information, refer to [1]_.
"""
if n < 0 or n >= nu:
return nan
elif n == 0:
moment = stats.t.cdf(z, nu)
elif n == 1:
c = gamma(0.5 * (nu + 1)) / (sqrt(nu * pi) * gamma(0.5 * nu))
e = 0.5 * (nu + 1)
moment = (0.5 * (c * nu) / (1 - e)) * ((1 + (z ** 2) / nu) ** (1 - e))
else:
t1 = (z ** (n - 1)) * (nu + z ** 2) * stats.t.pdf(z, nu)
t2 = (n - 1) * nu * StudentsT._ord_t_partial_moment(n - 2, z, nu)
moment = (1 / (n - nu)) * (t1 - t2)
return moment
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