Dynamic factor model
Parameters: | endog : array_like
exog : array_like, optional
k_factors : int
factor_order : int
error_cov_type : {‘scalar’, ‘diagonal’, ‘unstructured’}, optional
error_order : int, optional
error_var : boolean, optional
enforce_stationarity : boolean, optional
**kwargs :
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Notes
The dynamic factor model considered here is in the so-called static form, and is specified:
y_t & = \Lambda f_t + B x_t + u_t \\ f_t & = A_1 f_{t-1} + \dots + A_p f_{t-p} + \eta_t \\ u_t & = C_1 u_{t-1} + \dots + C_1 f_{t-q} + \varepsilon_t
where there are k_endog observed series and k_factors unobserved factors. Thus y_t is a k_endog x 1 vector and f_t is a k_factors x 1 vector.
x_t are optional exogenous vectors, shaped k_exog x 1.
\eta_t and \varepsilon_t are white noise error terms. In order to identify the factors, Var(\eta_t) = I. Denote Var(\varepsilon_t) \equiv \Sigma.
Options related to the unobserved factors:
Options related to the observation error term u_t:
References
[R60] | Lutkepohl, Helmut. 2007. New Introduction to Multiple Time Series Analysis. Berlin: Springer. |
Attributes
Methods
filter(params, **kwargs) | |
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 |
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 |
smooth(params, **kwargs) | |
transform_jacobian(unconstrained[, ...]) | Jacobian matrix for the parameter transformation function |
transform_params(unconstrained) | Transform unconstrained parameters used by the optimizer to constrained |
untransform_params(constrained) | Transform constrained parameters used in likelihood evaluation to unconstrained parameters used by the optimizer. |
update(params[, transformed, complex_step]) | Update the parameters of the model |
Methods
filter(params, **kwargs) | |
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 |
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 |
smooth(params, **kwargs) | |
transform_jacobian(unconstrained[, ...]) | Jacobian matrix for the parameter transformation function |
transform_params(unconstrained) | Transform unconstrained parameters used by the optimizer to constrained |
untransform_params(constrained) | Transform constrained parameters used in likelihood evaluation to unconstrained parameters used by the optimizer. |
update(params[, transformed, complex_step]) | Update the parameters of the model |
Attributes
endog_names | Names of endogenous variables |
exog_names | |
initial_variance | |
initialization | |
loglikelihood_burn | |
param_names | |
start_params | |
tolerance |