class statsmodels.tsa.vector_ar.vecm.VECM(endog, exog=None, exog_coint=None, dates=None, freq=None, missing='none', k_ar_diff=1, coint_rank=1, deterministic='nc', seasons=0, first_season=0)
[source]
Class representing a Vector Error Correction Model (VECM).
A VECM(\(k_{ar}-1\)) has the following form
where
as described in chapter 7 of [1].
Parameters: |
|
---|
A VECM(\(k_{ar} - 1\)) with deterministic terms has the form
In \(D^{co}_{t-1}\) we have the deterministic terms which are inside the cointegration relation (or restricted to the cointegration relation). \(\eta\) is the corresponding estimator. To pass a deterministic term inside the cointegration relation, we can use the exog_coint
argument. For the two special cases of an intercept and a linear trend there exists a simpler way to declare these terms: we can pass "ci"
and "li"
respectively to the deterministic
argument. So for an intercept inside the cointegration relation we can either pass "ci"
as deterministic
or np.ones(len(data))
as exog_coint
if data
is passed as the endog
argument. This ensures that \(D_{t-1}^{co} = 1\) for all \(t\).
We can also use deterministic terms outside the cointegration relation. These are defined in \(D_t\) in the formula above with the corresponding estimators in the matrix \(C\). We specify such terms by passing them to the exog
argument. For an intercept and/or linear trend we again have the possibility to use deterministic
alternatively. For an intercept we pass "co"
and for a linear trend we pass "lo"
where the o
stands for outside
.
The following table shows the five cases considered in [2]. The last column indicates which string to pass to the deterministic
argument for each of these cases.
Case | Intercept | Slope of the linear trend | deterministic |
---|---|---|---|
I | 0 | 0 | "nc" |
II | \(- \alpha \beta^T \mu\) | 0 | "ci" |
III | \(\neq 0\) | 0 | "co" |
IV | \(\neq 0\) | \(- \alpha \beta^T \gamma\) | "coli" |
V | \(\neq 0\) | \(\neq 0\) | "colo" |
[1] | Lütkepohl, H. 2005. New Introduction to Multiple Time Series Analysis. Springer. |
[2] | Johansen, S. 1995. Likelihood-Based Inference in Cointegrated * *Vector Autoregressive Models. Oxford University Press. |
fit ([method]) | Estimates the parameters of a VECM. |
from_formula (formula, data[, subset, drop_cols]) | Create a Model from a formula and dataframe. |
hessian (params) | The Hessian matrix of the model |
information (params) | Fisher information matrix of model |
initialize () | Initialize (possibly re-initialize) a Model instance. |
loglike (params) | Log-likelihood of model. |
predict (params[, exog]) | After a model has been fit predict returns the fitted values. |
score (params) | Score vector of model. |
endog_names | Names of endogenous variables |
exog_names |
© 2009–2012 Statsmodels Developers
© 2006–2008 Scipy Developers
© 2006 Jonathan E. Taylor
Licensed under the 3-clause BSD License.
http://www.statsmodels.org/stable/generated/statsmodels.tsa.vector_ar.vecm.VECM.html