def _eigval_decomp_SZ(self, irf_resim):
"""
Returns
-------
W: array of eigenvectors
eigva: list of eigenvalues
k: matrix indicating column # of largest eigenvalue for each c_i,j
"""
neqs = self.neqs
periods = self.periods
cov_hold = np.zeros((neqs, neqs, periods, periods))
for i in xrange(neqs):
for j in xrange(neqs):
cov_hold[i, j, :, :] = np.cov(irf_resim[:, 1:, i, j], rowvar=0)
W = np.zeros((neqs, neqs, periods, periods))
eigva = np.zeros((neqs, neqs, periods, 1))
k = np.zeros((neqs, neqs))
for i in xrange(neqs):
for j in xrange(neqs):
W[i, j, :, :], eigva[i, j, :, 0], k[i, j] = util.eigval_decomp(cov_hold[i, j, :, :])
return W, eigva, k
def _eigval_decomp_SZ(self, irf_resim):
"""
Returns
-------
W: array of eigenvectors
eigva: list of eigenvalues
k: matrix indicating column # of largest eigenvalue for each c_i,j
"""
neqs = self.neqs
periods = self.periods
cov_hold = np.zeros((neqs, neqs, periods, periods))
for i in xrange(neqs):
for j in xrange(neqs):
cov_hold[i,j,:,:] = np.cov(irf_resim[:,1:,i,j],rowvar=0)
W = np.zeros((neqs, neqs, periods, periods))
eigva = np.zeros((neqs, neqs, periods, 1))
k = np.zeros((neqs, neqs))
for i in xrange(neqs):
for j in xrange(neqs):
W[i,j,:,:], eigva[i,j,:,0], k[i,j] = util.eigval_decomp(cov_hold[i,j,:,:])
return W, eigva, k
def err_band_sz3(self, orth=False, repl=1000, signif=0.05, seed=None, burn=100, component=None):
"""
IRF Sims-Zha error band method 3. Does not assume symmetric error bands around mean.
Parameters
----------
orth : bool, default False
Compute orthogonalized impulse responses
repl : int, default 1000
Number of MC replications
signif : float (0 < signif < 1)
Significance level for error bars, defaults to 95% CI
seed : int, default None
np.random seed
burn : int, default 100
Number of initial simulated obs to discard
component : vector length neqs, default to largest for each
Index of column of eigenvector/value to use for each error band
Note: period of impulse (t=0) is not included when computing
principle component
Reference
---------
Sims, Christopher A., and Tao Zha. 1999. "Error Bands for Impulse
Response". Econometrica 67: 1113-1155.
"""
model = self.model
periods = self.periods
if orth:
irfs = self.orth_irfs
elif svar:
irfs = self.svar_irfs
else:
irfs = self.irfs
neqs = self.neqs
irf_resim = model.irf_resim(orth=orth, repl=repl, T=periods, seed=seed, burn=100)
stack = np.zeros((neqs, repl, periods * neqs))
# stack left to right, up and down
for p in xrange(repl):
for i in xrange(neqs):
stack[i, p, :] = np.ravel(irf_resim[p, 1:, :, i].T)
stack_cov = np.zeros((neqs, periods * neqs, periods * neqs))
W = np.zeros((neqs, periods * neqs, periods * neqs))
eigva = np.zeros((neqs, periods * neqs))
k = np.zeros((neqs))
if component != None:
if np.size(component) != (neqs):
raise ValueError("Component array must be of length " + str(neqs))
if np.argmax(component) >= neqs * periods:
raise ValueError("Atleast one of the components does not exist")
else:
k = component
# compute for eigen decomp for each stack
for i in xrange(neqs):
stack_cov[i] = np.cov(stack[i], rowvar=0)
W[i], eigva[i], k[i] = util.eigval_decomp(stack_cov[i])
gamma = np.zeros((repl, periods + 1, neqs, neqs))
for p in xrange(repl):
c = 0
for j in xrange(neqs):
for i in xrange(neqs):
gamma[p, 1:, i, j] = W[j, k[j], i * periods : (i + 1) * periods] * irf_resim[p, 1:, i, j]
if i == neqs - 1:
gamma[p, 1:, i, j] = W[j, k[j], i * periods :] * irf_resim[p, 1:, i, j]
gamma_sort = np.sort(gamma, axis=0) # sort to get quantiles
indx = round(signif / 2 * repl) - 1, round((1 - signif / 2) * repl) - 1
lower = np.copy(irfs)
upper = np.copy(irfs)
for i in xrange(neqs):
for j in xrange(neqs):
lower[:, i, j] = irfs[:, i, j] + gamma_sort[indx[0], :, i, j]
upper[:, i, j] = irfs[:, i, j] + gamma_sort[indx[1], :, i, j]
return lower, upper
def err_band_sz3(self, orth=False, repl=1000, signif=0.05,
seed=None, burn=100, component=None):
"""
IRF Sims-Zha error band method 3. Does not assume symmetric error bands around mean.
Parameters
----------
orth : bool, default False
Compute orthogonalized impulse responses
repl : int, default 1000
Number of MC replications
signif : float (0 < signif < 1)
Significance level for error bars, defaults to 95% CI
seed : int, default None
np.random seed
burn : int, default 100
Number of initial simulated obs to discard
component : vector length neqs, default to largest for each
Index of column of eigenvector/value to use for each error band
Note: period of impulse (t=0) is not included when computing
principle component
Reference
---------
Sims, Christoper A., and Tao Zha. 1999. “Error Bands for Impulse Response.” Econometrica 67: 1113-1155.
"""
model = self.model
periods = self.periods
if orth:
irfs = self.orth_irfs
elif svar:
irfs = self.svar_irfs
else:
irfs = self.irfs
neqs = self.neqs
irf_resim = model.irf_resim(orth=orth, repl=repl, T=periods, seed=seed,
burn=100)
stack = np.zeros((neqs, repl, periods*neqs))
#stack left to right, up and down
for p in xrange(repl):
for i in xrange(neqs):
stack[i, p,:] = np.ravel(irf_resim[p,1:,:,i].T)
stack_cov=np.zeros((neqs, periods*neqs, periods*neqs))
W = np.zeros((neqs, periods*neqs, periods*neqs))
eigva = np.zeros((neqs, periods*neqs))
k = np.zeros((neqs))
if component != None:
if np.size(component) != (neqs):
raise ValueError("Component array must be of length " + str(neqs))
if np.argmax(component) >= neqs*periods:
raise ValueError("Atleast one of the components does not exist")
else:
k = component
#compute for eigen decomp for each stack
for i in xrange(neqs):
stack_cov[i] = np.cov(stack[i],rowvar=0)
W[i], eigva[i], k[i] = util.eigval_decomp(stack_cov[i])
gamma = np.zeros((repl, periods+1, neqs, neqs))
for p in xrange(repl):
c=0
for j in xrange(neqs):
for i in xrange(neqs):
gamma[p,1:,i,j] = W[j,k[j],i*periods:(i+1)*periods] * irf_resim[p,1:,i,j]
if i == neqs-1:
gamma[p,1:,i,j] = W[j,k[j],i*periods:] * irf_resim[p,1:,i,j]
gamma_sort = np.sort(gamma, axis=0) #sort to get quantiles
indx = round(signif/2*repl)-1,round((1-signif/2)*repl)-1
lower = np.copy(irfs)
upper = np.copy(irfs)
for i in xrange(neqs):
for j in xrange(neqs):
lower[:,i,j] = irfs[:,i,j] + gamma_sort[indx[0],:,i,j]
upper[:,i,j] = irfs[:,i,j] + gamma_sort[indx[1],:,i,j]
return lower, upper