statsmodels.tsa.vector_ar.vecm.VECMResults¶
-
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]¶ Class for holding estimation related results of a vector error correction model (VECM).
- Parameters
- endog
ndarray
(neqs
x
nobs_tot
) Array of observations.
- exog
ndarray
(nobs_tot
x
neqs
)or
None Deterministic terms outside the cointegration relation.
- exog_coint
ndarray
(nobs_tot
x
neqs
)or
None Deterministic terms inside the cointegration relation.
- k_ar
int
, >= 1 Lags in the VAR representation. This implies that the number of lags in the VEC representation (=lagged differences) equals \(k_{ar} - 1\).
- coint_rank
int
, 0 <= coint_rank <=neqs
Cointegration rank, equals the rank of the matrix \(\Pi\) and the number of columns of \(\alpha\) and \(\beta\).
- alpha
ndarray
(neqs
x
coint_rank) Estimate for the parameter \(\alpha\) of a VECM.
- beta
ndarray
(neqs
x
coint_rank) Estimate for the parameter \(\beta\) of a VECM.
- gamma
ndarray
(neqs
x
neqs*(k_ar-1)) Array containing the estimates of the \(k_{ar}-1\) parameter matrices \(\Gamma_1, \dots, \Gamma_{k_{ar}-1}\) of a VECM(\(k_{ar}-1\)). The submatrices are stacked horizontally from left to right.
- sigma_u
ndarray
(neqs
x
neqs
) Estimate of white noise process covariance matrix \(\Sigma_u\).
- deterministic
str
{"nc"
,"co"
,"ci"
,"lo"
,"li"
} "nc"
- no deterministic terms"co"
- constant outside the cointegration relation"ci"
- constant within the cointegration relation"lo"
- linear trend outside the cointegration relation"li"
- linear trend within the cointegration relation
Combinations of these are possible (e.g.
"cili"
or"colo"
for linear trend with intercept). See the docstring of theVECM
-class for more information.- seasons
int
, default: 0 Number of periods in a seasonal cycle. 0 means no seasons.
- first_season
int
, default: 0 Season of the first observation.
- delta_y_1_T
ndarray
or None, default: None Auxiliary array for internal computations. It will be calculated if not given as parameter.
- y_lag1
ndarray
or None, default: None Auxiliary array for internal computations. It will be calculated if not given as parameter.
- delta_x
ndarray
or None, default: None Auxiliary array for internal computations. It will be calculated if not given as parameter.
- model
VECM
An instance of the
VECM
-class.- names
list
of
str
Each str in the list represents the name of a variable of the time series.
- datesarray_like
For example a DatetimeIndex of length nobs_tot.
- endog
References
- R4afe54e41569-1(1,2,3,4)
Lütkepohl, H. 2005. New Introduction to Multiple Time Series Analysis. Springer.
- Attributes
- nobs
int
Number of observations (excluding the presample).
- model
see
Parameters
- y_all
see
endogin
Parameters
- exog
see
Parameters
- exog_coint
see
Parameters
- names
see
Parameters
- dates
see
Parameters
- neqs
int
Number of variables in the time series.
- k_ar
see
Parameters
- deterministic
see
Parameters
- seasons
see
Parameters
- first_season
see
Parameters
- alpha
see
Parameters
- beta
see
Parameters
- gamma
see
Parameters
- sigma_u
see
Parameters
- 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
(1x
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
(1x
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.
- 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
- _y_lag1
see
y_lag1
in
Parameters
- _delta_x
see
delta_x
in
Parameters
- coint_rank
int
Cointegration rank, equals the rank of the matrix \(\Pi\) and the number of columns of \(\alpha\) and \(\beta\).
- llf
float
The model’s log-likelihood.
- 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 [R4afe54e41569-1] as \(\Sigma_{co}\) and its relationship to the ML-estimators can be seen in eq. (7.2.21) on p. 296 in [R4afe54e41569-1].
- 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 [R4afe54e41569-1].
- stderr_params
ndarray
(d
) Array containing the standard errors of \(\Pi\), \(\Gamma\), and estimated parameters related to deterministic terms.
- stderr_coint
ndarray
(neqs+num_det_coef_cointx
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 \(\Gamma_1, \ldots, \Gamma_{k_{ar}-1}\).
- 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.
- 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)) - tvalues_det_coef
ndarray
(neqs
x
det.terms
outside
the
coint.relation
) - 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)) - pvalues_det_coef
ndarray
(neqs
x
det.terms
outside
the
coint.relation
) - 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 viaA[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 [R4afe54e41569-1]. It is needed e.g. for impulse-response-analysis.
- fittedvalues
ndarray
(nobs
x
neqs
) The predicted in-sample values of the models’ endogenous variables.
- resid
ndarray
(nobs
x
neqs
) The residuals.
- nobs
Methods
conf_int_alpha
([alpha])conf_int_beta
([alpha])conf_int_det_coef
([alpha])conf_int_det_coef_coint
([alpha])conf_int_gamma
([alpha])irf
([periods])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.
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.
Properties
Gives the covariance matrix of the corresponding VAR-representation.
Return the in-sample values of endog calculated by the model.
Compute the VECM’s loglikelihood.
Return the difference between observed and fitted values.
Standard errors of beta and deterministic terms inside the cointegration relation.