statsmodels.tsa.vector_ar.vecm.VECMResults
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class statsmodels.tsa.vector_ar.vecm.VECMResults(endog, exog, exog_coint, k_ar, coint_rank, alpha, beta, gamma, sigma_u, deterministic='nc', seasons=0, first_season=0, delta_y_1_T=None, y_lag1=None, delta_x=None, model=None, names=None, dates=None)
[source]
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Class for holding estimation related results of a vector error correction model (VECM).
Parameters: |
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Returns: |
- **Attributes**
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nobs (int) – Number of observations (excluding the presample).
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model (see Parameters)
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y_all (see
endog in Parameters) -
exog (see Parameters)
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exog_coint (see Parameters)
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names (see Parameters)
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dates (see Parameters)
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neqs (int) – Number of variables in the time series.
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k_ar (see Parameters)
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deterministic (see Parameters)
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seasons (see Parameters)
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first_season (see Parameters)
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alpha (see Parameters)
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beta (see Parameters)
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gamma (see Parameters)
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sigma_u (see Parameters)
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det_coef_coint (ndarray (#(determinist. terms inside the coint. rel.) x
coint_rank )) – Estimated coefficients for the all deterministic terms inside the cointegration relation. -
const_coint (ndarray (1 x
coint_rank )) – If there is a constant deterministic term inside the cointegration relation, then const_coint is the first row of det_coef_coint . Otherwise it’s an ndarray of zeros. -
lin_trend_coint (ndarray (1 x
coint_rank )) – If there is a linear deterministic term inside the cointegration relation, then lin_trend_coint contains the corresponding estimated coefficients. As such it represents the corresponding row of det_coef_coint . If there is no linear deterministic term inside the cointegration relation, then lin_trend_coint is an ndarray of zeros. -
exog_coint_coefs (ndarray (exog_coint.shape[1] x
coint_rank ) or None ) – If deterministic terms inside the cointegration relation are passed via the exog_coint parameter, then exog_coint_coefs contains the corresponding estimated coefficients. As such exog_coint_coefs represents the last rows of det_coef_coint . If no deterministic terms were passed via the exog_coint parameter, this attribute is None . -
det_coef (ndarray (neqs x #(deterministic terms outside the coint. rel.))) – Estimated coefficients for the all deterministic terms outside the cointegration relation.
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const (ndarray (neqs x 1) or (neqs x 0)) – If a constant deterministic term outside the cointegration is specified within the deterministic parameter, then
const is the first column of det_coef_coint . Otherwise it’s an ndarray of size zero. -
seasonal (ndarray (neqs x seasons)) – If the
seasons parameter is > 0, then seasonal contains the estimated coefficients corresponding to the seasonal terms. Otherwise it’s an ndarray of size zero. -
lin_trend (ndarray (neqs x 1) or (neqs x 0)) – If a linear deterministic term outside the cointegration is specified within the deterministic parameter, then
lin_trend contains the corresponding estimated coefficients. As such it represents the corresponding column of det_coef_coint . If there is no linear deterministic term outside the cointegration relation, then lin_trend is an ndarray of size zero. -
exog_coefs (ndarray (neqs x exog_coefs.shape[1])) – If deterministic terms outside the cointegration relation are passed via the
exog parameter, then exog_coefs contains the corresponding estimated coefficients. As such exog_coefs represents the last columns of det_coef . If no deterministic terms were passed via the exog parameter, this attribute is an ndarray of size zero. -
_delta_y_1_T (see delta_y_1_T in Parameters)
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_y_lag1 (see y_lag1 in Parameters)
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_delta_x (see delta_x in Parameters)
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coint_rank (int) – Cointegration rank, equals the rank of the matrix \(\Pi\) and the number of columns of \(\alpha\) and \(\beta\).
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llf (float) – The model’s log-likelihood.
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cov_params (ndarray (d x d)) – Covariance matrix of the parameters. The number of rows and columns, d (used in the dimension specification of this argument), is equal to neqs * (neqs+num_det_coef_coint + neqs*(k_ar-1)+number of deterministic dummy variables outside the cointegration relation). For the case with no deterministic terms this matrix is defined on p. 287 in as \(\Sigma_{co}\) and its relationship to the ML-estimators can be seen in eq. (7.2.21) on p. 296 in .
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cov_params_wo_det (ndarray) – Covariance matrix of the parameters \(\tilde{\Pi}, \tilde{\Gamma}\) where \(\tilde{\Pi} = \tilde{\alpha} \tilde{\beta'}\). Equals
cov_params without the rows and columns related to deterministic terms. This matrix is defined as \(\Sigma_{co}\) on p. 287 in . -
stderr_params (ndarray (d)) – Array containing the standard errors of \(\Pi\), \(\Gamma\), and estimated parameters related to deterministic terms.
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stderr_coint (ndarray (neqs+num_det_coef_coint x
coint_rank )) – Array containing the standard errors of \(\beta\) and estimated parameters related to deterministic terms inside the cointegration relation. -
stderr_alpha (ndarray (neqs x
coint_rank )) – The standard errors of \(\alpha\). -
stderr_beta (ndarray (neqs x
coint_rank )) – The standard errors of \(\beta\). -
stderr_det_coef_coint (ndarray (num_det_coef_coint x
coint_rank )) – The standard errors of estimated the parameters related to deterministic terms inside the cointegration relation. -
stderr_gamma (ndarray (neqs x neqs*(k_ar-1))) – The standard errors of \(\Gamma_1, \ldots, \Gamma_{k_{ar}-1}\).
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stderr_det_coef (ndarray (neqs x det. terms outside the coint. relation)) – The standard errors of estimated the parameters related to deterministic terms outside the cointegration relation.
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tvalues_alpha (ndarray (neqs x
coint_rank )) -
tvalues_beta (ndarray (neqs x
coint_rank )) -
tvalues_det_coef_coint (ndarray (num_det_coef_coint x
coint_rank )) -
tvalues_gamma (ndarray (neqs x neqs*(k_ar-1)))
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tvalues_det_coef (ndarray (neqs x det. terms outside the coint. relation))
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pvalues_alpha (ndarray (neqs x
coint_rank )) -
pvalues_beta (ndarray (neqs x
coint_rank )) -
pvalues_det_coef_coint (ndarray (num_det_coef_coint x
coint_rank )) -
pvalues_gamma (ndarray (neqs x neqs*(k_ar-1)))
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pvalues_det_coef (ndarray (neqs x det. terms outside the coint. relation))
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var_rep ((k_ar x neqs x neqs)) – KxK parameter matrices \(A_i\) of the corresponding VAR representation. If the return value is assigned to a variable
A , these matrices can be accessed via A[i] for \(i=0, \ldots, k_{ar}-1\). -
cov_var_repr (ndarray (neqs**2 * k_ar x neqs**2 * k_ar)) – This matrix is called \(\Sigma^{co}_{\alpha}\) on p. 289 in . It is needed e.g. for impulse-response-analysis.
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fittedvalues (ndarray (nobs x neqs)) – The predicted in-sample values of the models’ endogenous variables.
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resid (ndarray (nobs x neqs)) – The residuals.
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References
Methods
conf_int_alpha ([alpha]) | |
conf_int_beta ([alpha]) | |
conf_int_det_coef ([alpha]) | |
conf_int_det_coef_coint ([alpha]) | |
conf_int_gamma ([alpha]) | |
cov_params_default () | |
cov_params_wo_det () | |
cov_var_repr () | Gives the covariance matrix of the corresponding VAR-representation. |
fittedvalues () | Return the in-sample values of endog calculated by the model. |
irf ([periods]) | |
llf () | Compute the VECM’s loglikelihood. |
ma_rep ([maxn]) | |
orth_ma_rep ([maxn, P]) | Compute orthogonalized MA coefficient matrices. |
plot_data ([with_presample]) | Plot the input time series. |
plot_forecast (steps[, alpha, plot_conf_int, …]) | Plot the forecast. |
predict ([steps, alpha, exog_fc, exog_coint_fc]) | Calculate future values of the time series. |
pvalues_alpha () | |
pvalues_beta () | |
pvalues_det_coef () | |
pvalues_det_coef_coint () | |
pvalues_gamma () | |
resid () | Return the difference between observed and fitted values. |
stderr_alpha () | |
stderr_beta () | |
stderr_coint () | Standard errors of beta and deterministic terms inside the cointegration relation. |
stderr_det_coef () | |
stderr_det_coef_coint () | |
stderr_gamma () | |
stderr_params () | |
summary ([alpha]) | Return a summary of the estimation results. |
test_granger_causality (caused[, causing, signif]) | Test for Granger-causality. |
test_inst_causality (causing[, signif]) | Test for instantaneous causality. |
test_normality ([signif]) | Test assumption of normal-distributed errors using Jarque-Bera-style omnibus \(\chi^2\) test. |
test_whiteness ([nlags, signif, adjusted]) | Test the whiteness of the residuals using the Portmanteau test. |
tvalues_alpha () | |
tvalues_beta () | |
tvalues_det_coef () | |
tvalues_det_coef_coint () | |
tvalues_gamma () | |
var_rep () | |