def plot_with_error(y,
error,
x=None,
axes=None,
value_fmt='k',
error_fmt='k--',
alpha=0.05,
stderr_type='asym'):
"""
Make plot with optional error bars
Parameters
----------
y :
error : array or None
"""
import matplotlib.pyplot as plt
if axes is None:
axes = plt.gca()
x = x if x is not None else lrange(len(y))
plot_action = lambda y, fmt: axes.plot(x, y, fmt)
plot_action(y, value_fmt)
#changed this
if error is not None:
if stderr_type == 'asym':
q = util.norm_signif_level(alpha)
plot_action(y - q * error, error_fmt)
plot_action(y + q * error, error_fmt)
if stderr_type in ('mc', 'sz1', 'sz2', 'sz3'):
plot_action(error[0], error_fmt)
plot_action(error[1], error_fmt)
def plot_with_error(y, error, x=None, axes=None, value_fmt='k',
error_fmt='k--', alpha=0.05, stderr_type = 'asym'):
"""
Make plot with optional error bars
Parameters
----------
y :
error : array or None
"""
import matplotlib.pyplot as plt
if axes is None:
axes = plt.gca()
x = x if x is not None else range(len(y))
plot_action = lambda y, fmt: axes.plot(x, y, fmt)
plot_action(y, value_fmt)
#changed this
if error is not None:
if stderr_type == 'asym':
q = util.norm_signif_level(alpha)
plot_action(y - q * error, error_fmt)
plot_action(y + q * error, error_fmt)
if stderr_type in ('mc','sz1','sz2','sz3'):
plot_action(error[0], error_fmt)
plot_action(error[1], error_fmt)
def err_band_sz1(self, orth=False, svar=False, repl=1000,
signif=0.05, seed=None, burn=100, component=None):
"""
IRF Sims-Zha error band method 1. Assumes 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 : neqs x neqs array, 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
References
----------
Sims, Christopher A., and Tao Zha. 1999. "Error Bands for Impulse
Response". Econometrica 67: 1113-1155.
"""
model = self.model
periods = self.periods
irfs = self._choose_irfs(orth, svar)
neqs = self.neqs
irf_resim = model.irf_resim(orth=orth, repl=repl, T=periods, seed=seed,
burn=100)
q = util.norm_signif_level(signif)
W, eigva, k =self._eigval_decomp_SZ(irf_resim)
if component is not None:
if np.shape(component) != (neqs,neqs):
raise ValueError("Component array must be " + str(neqs) + " x " + str(neqs))
if np.argmax(component) >= neqs*periods:
raise ValueError("Atleast one of the components does not exist")
else:
k = component
# here take the kth column of W, which we determine by finding the largest eigenvalue of the covaraince matrix
lower = np.copy(irfs)
upper = np.copy(irfs)
for i in range(neqs):
for j in range(neqs):
lower[1:,i,j] = irfs[1:,i,j] + W[i,j,:,k[i,j]]*q*np.sqrt(eigva[i,j,k[i,j]])
upper[1:,i,j] = irfs[1:,i,j] - W[i,j,:,k[i,j]]*q*np.sqrt(eigva[i,j,k[i,j]])
return lower, upper
def err_band_sz1(self, orth=False, svar=False, repl=1000,
signif=0.05, seed=None, burn=100, component=None):
"""
IRF Sims-Zha error band method 1. Assumes 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 : neqs x neqs array, 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
References
----------
Sims, Christopher A., and Tao Zha. 1999. "Error Bands for Impulse
Response". Econometrica 67: 1113-1155.
"""
model = self.model
periods = self.periods
irfs = self._choose_irfs(orth, svar)
neqs = self.neqs
irf_resim = model.irf_resim(orth=orth, repl=repl, T=periods, seed=seed,
burn=100)
q = util.norm_signif_level(signif)
W, eigva, k =self._eigval_decomp_SZ(irf_resim)
if component is not None:
if np.shape(component) != (neqs,neqs):
raise ValueError("Component array must be " + str(neqs) + " x " + str(neqs))
if np.argmax(component) >= neqs*periods:
raise ValueError("Atleast one of the components does not exist")
else:
k = component
# here take the kth column of W, which we determine by finding the largest eigenvalue of the covaraince matrix
lower = np.copy(irfs)
upper = np.copy(irfs)
for i in range(neqs):
for j in range(neqs):
lower[1:,i,j] = irfs[1:,i,j] + W[i,j,:,k[i,j]]*q*np.sqrt(eigva[i,j,k[i,j]])
upper[1:,i,j] = irfs[1:,i,j] - W[i,j,:,k[i,j]]*q*np.sqrt(eigva[i,j,k[i,j]])
return lower, upper
def forecast_interval(self, y, steps, alpha=0.05):
"""Construct forecast interval estimates assuming the y are Gaussian
Parameters
----------
Notes
-----
Lutkepohl pp. 39-40
Returns
-------
(lower, mid, upper) : (ndarray, ndarray, ndarray)
"""
assert(0 < alpha < 1)
q = util.norm_signif_level(alpha)
point_forecast = self.forecast(y, steps)
sigma = np.sqrt(self._forecast_vars(steps))
forc_lower = point_forecast - q * sigma
forc_upper = point_forecast + q * sigma
return point_forecast, forc_lower, forc_upper