def var_loglike(resid, omega, nobs):
r"""
Returns the value of the VAR(p) log-likelihood.
Parameters
----------
resid : ndarray (T x K)
omega : ndarray
Sigma hat matrix. Each element i,j is the average product of the
OLS residual for variable i and the OLS residual for variable j or
np.dot(resid.T,resid)/nobs. There should be no correction for the
degrees of freedom.
nobs : int
Returns
-------
llf : float
The value of the loglikelihood function for a VAR(p) model
Notes
-----
The loglikelihood function for the VAR(p) is
.. math::
-\left(\frac{T}{2}\right)
\left(\ln\left|\Omega\right|-K\ln\left(2\pi\right)-K\right)
"""
logdet = util.get_logdet(np.asarray(omega))
neqs = len(omega)
part1 = - (nobs * neqs / 2) * np.log(2 * np.pi)
part2 = - (nobs / 2) * (logdet + neqs)
return part1 + part2
def var_loglike(resid, omega, nobs):
r"""
Returns the value of the VAR(p) log-likelihood.
Parameters
----------
resid : ndarray (T x K)
omega : ndarray
Sigma hat matrix. Each element i,j is the average product of the
OLS residual for variable i and the OLS residual for variable j or
np.dot(resid.T,resid)/nobs. There should be no correction for the
degrees of freedom.
nobs : int
Returns
-------
llf : float
The value of the loglikelihood function for a VAR(p) model
Notes
-----
The loglikelihood function for the VAR(p) is
.. math::
-\left(\frac{T}{2}\right)
\left(\ln\left|\Omega\right|-K\ln\left(2\pi\right)-K\right)
"""
logdet = util.get_logdet(np.asarray(omega))
neqs = len(omega)
part1 = -(nobs * neqs / 2) * np.log(2 * np.pi)
part2 = -(nobs / 2) * (logdet + neqs)
return part1 + part2
def info_criteria(self):
"information criteria for lagorder selection"
nobs = self.nobs
neqs = self.neqs
lag_order = self.k_ar
free_params = lag_order * neqs**2 + neqs * self.k_trend
ld = util.get_logdet(self.sigma_u_mle)
# See Lutkepohl pp. 146-150
aic = ld + (2. / nobs) * free_params
bic = ld + (np.log(nobs) / nobs) * free_params
hqic = ld + (2. * np.log(np.log(nobs)) / nobs) * free_params
fpe = ((nobs + self.df_model) / self.df_resid)**neqs * np.exp(ld)
return {'aic': aic, 'bic': bic, 'hqic': hqic, 'fpe': fpe}
def info_criteria(self):
"information criteria for lagorder selection"
nobs = self.nobs
neqs = self.neqs
lag_order = self.k_ar
free_params = lag_order * neqs ** 2 + neqs * self.k_trend
ld = util.get_logdet(self.sigma_u_mle)
# See Lutkepohl pp. 146-150
aic = ld + (2. / nobs) * free_params
bic = ld + (np.log(nobs) / nobs) * free_params
hqic = ld + (2. * np.log(np.log(nobs)) / nobs) * free_params
fpe = ((nobs + self.df_model) / self.df_resid) ** neqs * np.exp(ld)
return {
'aic' : aic,
'bic' : bic,
'hqic' : hqic,
'fpe' : fpe
}