statsmodels.tsa.statespace.tools.constrain_stationary_multivariate(unconstrained, variance, transform_variance=False, prefix=None)
[source]
Transform unconstrained parameters used by the optimizer to constrained parameters used in likelihood evaluation for a vector autoregression.
Parameters: |
|
---|---|
Returns: |
constrained – Transformed coefficient matrices leading to a stationary VAR representation. Will match the type of the passed |
Return type: |
array or list |
In the notation of [1], the arguments (variance, unconstrained)
are written as \((\Sigma, A_1, \dots, A_p)\), where \(p\) is the order of the vector autoregression, and is here determined by the length of the unconstrained
argument.
There are two steps in the constraining algorithm.
First, \((A_1, \dots, A_p)\) are transformed into \((P_1, \dots, P_p)\) via Lemma 2.2 of [1].
Second, \((\Sigma, P_1, \dots, P_p)\) are transformed into \((\Sigma, \phi_1, \dots, \phi_p)\) via Lemmas 2.1 and 2.3 of [1].
If transform_variance=True
, then only Lemma 2.1 is applied in the second step.
While this function can be used even in the univariate case, it is much slower, so in that case constrain_stationary_univariate
is preferred.
[1] | (1, 2, 3) Ansley, Craig F., and Robert Kohn. 1986. “A Note on Reparameterizing a Vector Autoregressive Moving Average Model to Enforce Stationarity.” Journal of Statistical Computation and Simulation 24 (2): 99-106. |
[*] | Ansley, Craig F, and Paul Newbold. 1979. “Multivariate Partial Autocorrelations.” In Proceedings of the Business and Economic Statistics Section, 349-53. American Statistical Association |
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© 2006–2008 Scipy Developers
© 2006 Jonathan E. Taylor
Licensed under the 3-clause BSD License.
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