def __init__(self, model, P=None, periods=10, order=None):
self.model = model
self.periods = periods
self.neqs, self.lags, self.T = model.neqs, model.k_ar, model.nobs
self.order = order
if P is None:
sigma = model.sigma_u
# TODO, may be difficult at the moment
# if order is not None:
# indexer = [model.get_eq_index(name) for name in order]
# sigma = sigma[:, indexer][indexer, :]
# if sigma.shape != model.sigma_u.shape:
# raise ValueError('variable order is wrong length')
P = la.cholesky(sigma)
self.P = P
self.irfs = model.ma_rep(periods)
self.orth_irfs = model.orth_ma_rep(periods)
self.cum_effects = self.irfs.cumsum(axis=0)
self.orth_cum_effects = self.orth_irfs.cumsum(axis=0)
self.lr_effects = model.long_run_effects()
self.orth_lr_effects = np.dot(model.long_run_effects(), P)
# auxiliary stuff
self._A = util.comp_matrix(model.coefs)
def __init__(self, model, P=None, periods=10, order=None):
self.model = model
self.periods = periods
self.neqs, self.lags, self.T = model.neqs, model.k_ar, model.nobs
self.order = order
if P is None:
sigma = model.sigma_u
# TODO, may be difficult at the moment
# if order is not None:
# indexer = [model.get_eq_index(name) for name in order]
# sigma = sigma[:, indexer][indexer, :]
# if sigma.shape != model.sigma_u.shape:
# raise ValueError('variable order is wrong length')
P = la.cholesky(sigma)
self.P = P
self.irfs = model.ma_rep(periods)
self.orth_irfs = model.orth_ma_rep(periods)
self.cum_effects = self.irfs.cumsum(axis=0)
self.orth_cum_effects = self.orth_irfs.cumsum(axis=0)
self.lr_effects = model.long_run_effects()
self.orth_lr_effects = np.dot(model.long_run_effects(), P)
# auxiliary stuff
self._A = util.comp_matrix(model.coefs)
def is_stable(coefs, verbose=False):
"""
Determine stability of VAR(p) system by examining the eigenvalues of the
VAR(1) representation
Parameters
----------
coefs : ndarray (p x k x k)
Returns
-------
is_stable : bool
"""
A_var1 = util.comp_matrix(coefs)
eigs = np.linalg.eigvals(A_var1)
if verbose:
print 'Eigenvalues of VAR(1) rep'
for val in np.abs(eigs):
print val
return (np.abs(eigs) <= 1).all()
def is_stable(coefs, verbose=False):
"""
Determine stability of VAR(p) system by examining the eigenvalues of the
VAR(1) representation
Parameters
----------
coefs : ndarray (p x k x k)
Returns
-------
is_stable : bool
"""
A_var1 = util.comp_matrix(coefs)
eigs = np.linalg.eigvals(A_var1)
if verbose:
print 'Eigenvalues of VAR(1) rep'
for val in np.abs(eigs):
print val
return (np.abs(eigs) <= 1).all()
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 _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