def _forecast_cov_resid_raw(self, h):
"""
Returns the covariance of the residual errors for the forecast at
1, 2, ..., h timesteps.
"""
psi_values = self._psi(h)
sum = 0
result = []
for i in xrange(h):
psi = psi_values[i]
sum = sum + chain_dot(psi, self._sigma, psi.T)
result.append(sum)
return result
def _forecast_cov_resid_raw(self, h):
"""
Returns the covariance of the residual errors for the forecast at
1, 2, ..., h timesteps.
"""
psi_values = self._psi(h)
sum = 0
result = []
for i in xrange(h):
psi = psi_values[i]
sum = sum + chain_dot(psi, self._sigma, psi.T)
result.append(sum)
return result
def _forecast_cov_beta_raw(self, n):
"""
Returns the covariance of the beta errors for the forecast at
1, 2, ..., n timesteps.
"""
p = self._p
values = self._data.values
T = len(values) - self._p - 1
results = []
for h in xrange(1, n + 1):
psi = self._psi(h)
trans_B = self._trans_B(h)
sum = 0
cov_beta = self._cov_beta
for t in xrange(T + 1):
index = t + p
y = values.take(xrange(index, index - p, -1), axis=0).flatten()
trans_Z = np.hstack(([1], y))
trans_Z = trans_Z.reshape(1, len(trans_Z))
sum2 = 0
for i in xrange(h):
ZB = np.dot(trans_Z, trans_B[h - 1 - i])
prod = np.kron(ZB, psi[i])
sum2 = sum2 + prod
sum = sum + chain_dot(sum2, cov_beta, sum2.T)
results.append(sum / (T + 1))
return results
def _forecast_cov_beta_raw(self, n):
"""
Returns the covariance of the beta errors for the forecast at
1, 2, ..., n timesteps.
"""
p = self._p
values = self._data.values
T = len(values) - self._p - 1
results = []
for h in xrange(1, n + 1):
psi = self._psi(h)
trans_B = self._trans_B(h)
sum = 0
cov_beta = self._cov_beta
for t in xrange(T + 1):
index = t + p
y = values.take(xrange(index, index - p, -1), axis=0).flatten()
trans_Z = np.hstack(([1], y))
trans_Z = trans_Z.reshape(1, len(trans_Z))
sum2 = 0
for i in xrange(h):
ZB = np.dot(trans_Z, trans_B[h - 1 - i])
prod = np.kron(ZB, psi[i])
sum2 = sum2 + prod
sum = sum + chain_dot(sum2, cov_beta, sum2.T)
results.append(sum / (T + 1))
return results
