class statsmodels.tsa.statespace.varmax.VARMAX(endog, exog=None, order=(1, 0), trend='c', error_cov_type='unstructured', measurement_error=False, enforce_stationarity=True, enforce_invertibility=True, **kwargs)
[source]
Vector Autoregressive Moving Average with eXogenous regressors model
Parameters: |
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order
iterable – The (p,q) order of the model for the number of AR and MA parameters to use.
trend
{‘nc’, ‘c’}, optional – Parameter controlling the deterministic trend polynomial. Can be specified as a string where ‘c’ indicates a constant intercept and ‘nc’ indicates no intercept term.
error_cov_type
{‘diagonal’, ‘unstructured’}, optional – The structure of the covariance matrix of the error term, where “unstructured” puts no restrictions on the matrix and “diagonal” requires it to be a diagonal matrix (uncorrelated errors). Default is “unstructured”.
measurement_error
boolean, optional – Whether or not to assume the endogenous observations endog
were measured with error. Default is False.
enforce_stationarity
boolean, optional – Whether or not to transform the AR parameters to enforce stationarity in the autoregressive component of the model. Default is True.
enforce_invertibility
boolean, optional – Whether or not to transform the MA parameters to enforce invertibility in the moving average component of the model. Default is True.
Generically, the VARMAX model is specified (see for example chapter 18 of [1]):
where \(\epsilon_t \sim N(0, \Omega)\), and where \(y_t\) is a k_endog x 1
vector. Additionally, this model allows considering the case where the variables are measured with error.
Note that in the full VARMA(p,q) case there is a fundamental identification problem in that the coefficient matrices \(\{A_i, M_j\}\) are not generally unique, meaning that for a given time series process there may be multiple sets of matrices that equivalently represent it. See Chapter 12 of [1] for more informationl. Although this class can be used to estimate VARMA(p,q) models, a warning is issued to remind users that no steps have been taken to ensure identification in this case.
[1] | (1, 2) Lütkepohl, Helmut. 2007. New Introduction to Multiple Time Series Analysis. Berlin: Springer. |
filter (params[, transformed, complex_step, …]) | Kalman filtering |
fit ([start_params, transformed, cov_type, …]) | Fits the model by maximum likelihood via Kalman filter. |
from_formula (formula, data[, subset]) | Not implemented for state space models |
hessian (params, *args, **kwargs) | Hessian matrix of the likelihood function, evaluated at the given parameters |
impulse_responses (params[, steps, impulse, …]) | Impulse response function |
information (params) | Fisher information matrix of model |
initialize () | Initialize (possibly re-initialize) a Model instance. |
initialize_approximate_diffuse ([variance]) | |
initialize_known (initial_state, …) | |
initialize_statespace (**kwargs) | Initialize the state space representation |
initialize_stationary () | |
loglike (params, *args, **kwargs) | Loglikelihood evaluation |
loglikeobs (params[, transformed, complex_step]) | Loglikelihood evaluation |
observed_information_matrix (params[, …]) | Observed information matrix |
opg_information_matrix (params[, …]) | Outer product of gradients information matrix |
predict (params[, exog]) | After a model has been fit predict returns the fitted values. |
prepare_data () | Prepare data for use in the state space representation |
score (params, *args, **kwargs) | Compute the score function at params. |
score_obs (params[, method, transformed, …]) | Compute the score per observation, evaluated at params |
set_conserve_memory ([conserve_memory]) | Set the memory conservation method |
set_filter_method ([filter_method]) | Set the filtering method |
set_inversion_method ([inversion_method]) | Set the inversion method |
set_smoother_output ([smoother_output]) | Set the smoother output |
set_stability_method ([stability_method]) | Set the numerical stability method |
simulate (params, nsimulations[, …]) | Simulate a new time series following the state space model |
simulation_smoother ([simulation_output]) | Retrieve a simulation smoother for the state space model. |
smooth (params[, transformed, complex_step, …]) | Kalman smoothing |
transform_jacobian (unconstrained[, …]) | Jacobian matrix for the parameter transformation function |
transform_params (unconstrained) | Transform unconstrained parameters used by the optimizer to constrained parameters used in likelihood evaluation |
untransform_params (constrained) | Transform constrained parameters used in likelihood evaluation to unconstrained parameters used by the optimizer. |
update (params, **kwargs) | Update the parameters of the model |
endog_names | Names of endogenous variables |
exog_names | |
initial_variance | |
initialization | |
loglikelihood_burn | |
param_names | (list of str) List of human readable parameter names (for parameters actually included in the model). |
start_params | (array) Starting parameters for maximum likelihood estimation. |
tolerance |
© 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.statespace.varmax.VARMAX.html