def start_params(self):
params = np.zeros(self.k_params, dtype=np.float64)
# A. Run a multivariate regression to get beta estimates
endog = self.endog.copy()
exog = self.exog.copy() if self.k_exog > 0 else None
# Although the Kalman filter can deal with missing values in endog,
# conditional sum of squares cannot
if np.any(np.isnan(endog)):
endog = endog[~np.isnan(endog)]
if exog is not None:
exog = exog[~np.isnan(endog)]
# Regression effects via OLS
exog_params = np.zeros(0)
if self.k_exog > 0:
exog_params = np.linalg.pinv(exog).dot(endog).T
endog -= np.dot(exog, exog_params.T)
# B. Run a VAR model on endog to get trend, AR parameters
ar_params = []
k_ar = self.k_ar if self.k_ar > 0 else 1
mod_ar = var_model.VAR(endog)
res_ar = mod_ar.fit(maxlags=k_ar, ic=None, trend=self.trend)
ar_params = np.array(res_ar.params.T)
if self.trend == 'c':
trend_params = ar_params[:, 0]
if self.k_ar > 0:
ar_params = ar_params[:, 1:].ravel()
else:
ar_params = []
elif self.k_ar > 0:
ar_params = ar_params.ravel()
else:
ar_params = []
endog = res_ar.resid
# Test for stationarity
if self.k_ar > 0 and self.enforce_stationarity:
coefficient_matrices = (
ar_params.reshape(
self.k_endog * self.k_ar, self.k_endog
).T
).reshape(self.k_endog, self.k_endog, self.k_ar).T
stationary = is_invertible([1] + list(-coefficient_matrices))
if not stationary:
raise ValueError('Non-stationary starting autoregressive'
' parameters found with `enforce_stationarity`'
' set to True.')
# C. Run a VAR model on the residuals to get MA parameters
ma_params = []
if self.k_ma > 0:
mod_ma = var_model.VAR(endog)
res_ma = mod_ma.fit(maxlags=self.k_ma, ic=None, trend='nc')
ma_params = np.array(res_ma.params.T).ravel()
# Test for invertibility
if self.enforce_invertibility:
coefficient_matrices = (
ma_params.reshape(
self.k_endog * self.k_ma, self.k_endog
).T
).reshape(self.k_endog, self.k_endog, self.k_ma).T
invertible = is_invertible([1] + list(-coefficient_matrices))
if not invertible:
raise ValueError('Non-invertible starting moving-average'
' parameters found with `enforce_stationarity`'
' set to True.')
# 1. Intercept terms
if self.trend == 'c':
params[self._params_trend] = trend_params
# 2. AR terms
params[self._params_ar] = ar_params
# 3. MA terms
params[self._params_ma] = ma_params
# 4. Regression terms
if self.mle_regression:
params[self._params_regression] = exog_params.ravel()
# 5. State covariance terms
if self.error_cov_type == 'diagonal':
params[self._params_state_cov] = res_ar.sigma_u.diagonal()
elif self.error_cov_type == 'unstructured':
cov_factor = np.linalg.cholesky(res_ar.sigma_u)
params[self._params_state_cov] = (
cov_factor[self._idx_lower_state_cov].ravel())
# 5. Measurement error variance terms
if self.measurement_error:
if self.k_ma > 0:
params[self._params_obs_cov] = res_ma.sigma_u.diagonal()
else:
params[self._params_obs_cov] = res_ar.sigma_u.diagonal()
return params
def test_cases(self):
for polynomial, invertible in self.cases:
assert_equal(tools.is_invertible(polynomial), invertible)
def test_cases(self):
for polynomial, invertible in self.cases:
assert_equal(tools.is_invertible(polynomial), invertible)
def start_params(self):
params = np.zeros(self.k_params, dtype=np.float64)
# A. Run a multivariate regression to get beta estimates
endog = self.endog.copy()
exog = self.exog.copy() if self.k_exog > 0 else None
# Although the Kalman filter can deal with missing values in endog,
# conditional sum of squares cannot
if np.any(np.isnan(endog)):
endog = endog[~np.isnan(endog)]
if exog is not None:
exog = exog[~np.isnan(endog)]
# Regression effects via OLS
exog_params = np.zeros(0)
if self.k_exog > 0:
exog_params = np.linalg.pinv(exog).dot(endog).T
endog -= np.dot(exog, exog_params.T)
# B. Run a VAR model on endog to get trend, AR parameters
ar_params = []
k_ar = self.k_ar if self.k_ar > 0 else 1
mod_ar = var_model.VAR(endog)
res_ar = mod_ar.fit(maxlags=k_ar, ic=None, trend=self.trend)
ar_params = np.array(res_ar.params.T)
if self.trend == 'c':
trend_params = ar_params[:, 0]
if self.k_ar > 0:
ar_params = ar_params[:, 1:].ravel()
else:
ar_params = []
elif self.k_ar > 0:
ar_params = ar_params.ravel()
else:
ar_params = []
endog = res_ar.resid
# Test for stationarity
if self.k_ar > 0 and self.enforce_stationarity:
coefficient_matrices = (ar_params.reshape(self.k_endog * self.k_ar,
self.k_endog).T).reshape(
self.k_endog,
self.k_endog,
self.k_ar).T
stationary = is_invertible([1] + list(-coefficient_matrices))
if not stationary:
raise ValueError(
'Non-stationary starting autoregressive'
' parameters found with `enforce_stationarity`'
' set to True.')
# C. Run a VAR model on the residuals to get MA parameters
ma_params = []
if self.k_ma > 0:
mod_ma = var_model.VAR(endog)
res_ma = mod_ma.fit(maxlags=self.k_ma, ic=None, trend='nc')
ma_params = np.array(res_ma.params.T).ravel()
# Test for invertibility
if self.enforce_invertibility:
coefficient_matrices = (ma_params.reshape(
self.k_endog * self.k_ma,
self.k_endog).T).reshape(self.k_endog, self.k_endog,
self.k_ma).T
invertible = is_invertible([1] + list(-coefficient_matrices))
if not invertible:
raise ValueError(
'Non-invertible starting moving-average'
' parameters found with `enforce_stationarity`'
' set to True.')
# 1. Intercept terms
if self.trend == 'c':
params[self._params_trend] = trend_params
# 2. AR terms
params[self._params_ar] = ar_params
# 3. MA terms
params[self._params_ma] = ma_params
# 4. Regression terms
if self.mle_regression:
params[self._params_regression] = exog_params.ravel()
# 5. State covariance terms
if self.error_cov_type == 'diagonal':
params[self._params_state_cov] = res_ar.sigma_u.diagonal()
elif self.error_cov_type == 'unstructured':
cov_factor = np.linalg.cholesky(res_ar.sigma_u)
params[self._params_state_cov] = (
cov_factor[self._idx_lower_state_cov].ravel())
# 5. Measurement error variance terms
if self.measurement_error:
if self.k_ma > 0:
params[self._params_obs_cov] = res_ma.sigma_u.diagonal()
else:
params[self._params_obs_cov] = res_ar.sigma_u.diagonal()
return params