def _var_acf(coefs, sig_u):
"""
Compute autocovariance function ACF_y(h) for h=1,...,p
Notes
-----
Lutkepohl (2005) p.29
"""
p, k, k2 = coefs.shape
assert(k == k2)
A = util.comp_matrix(coefs)
# construct VAR(1) noise covariance
SigU = np.zeros((k*p, k*p))
SigU[:k,:k] = sig_u
# vec(ACF) = (I_(kp)^2 - kron(A, A))^-1 vec(Sigma_U)
vecACF = L.solve(np.eye((k*p)**2) - np.kron(A, A), vec(SigU))
acf = unvec(vecACF)
acf = acf[:k].T.reshape((p, k, k))
return acf
def lr_effect_stderr(self, orth=False):
cov = self.lr_effect_cov(orth=orth)
return tsa.unvec(np.sqrt(np.diag(cov)))
def cum_effect_stderr(self, orth=False):
return np.array([tsa.unvec(np.sqrt(np.diag(c)))
for c in self.cum_effect_cov(orth=orth)])
def cum_effect_stderr(self, orth=False):
return np.array([
tsa.unvec(np.sqrt(np.diag(c)))
for c in self.cum_effect_cov(orth=orth)
])
def lr_effect_stderr(self, orth=False):
cov = self.lr_effect_cov(orth=orth)
return tsa.unvec(np.sqrt(np.diag(cov)))