statsmodels.tsa.statespace.kalman_smoother.KalmanSmoother.impulse_responses

KalmanSmoother.impulse_responses(steps=10, impulse=0, orthogonalized=False, cumulative=False, **kwargs)

Impulse response function

Parameters:

• steps (int, optional) – The number of steps for which impulse responses are calculated. Default is 10. Note that the initial impulse is not counted as a step, so if steps=1, the output will have 2 entries.
• impulse (int or array_like) – If an integer, the state innovation to pulse; must be between 0 and k_posdef-1 where k_posdef is the same as in the state space model. Alternatively, a custom impulse vector may be provided; must be a column vector with shape (k_posdef, 1).
• orthogonalized (boolean, optional) – Whether or not to perform impulse using orthogonalized innovations. Note that this will also affect custum impulse vectors. Default is False.
• cumulative (boolean, optional) – Whether or not to return cumulative impulse responses. Default is False.
• **kwargs – If the model is time-varying and steps is greater than the number of observations, any of the state space representation matrices that are time-varying must have updated values provided for the out-of-sample steps. For example, if design is a time-varying component, nobs is 10, and steps is 15, a (k_endog x k_states x 5) matrix must be provided with the new design matrix values.

Returns:

impulse_responses – Responses for each endogenous variable due to the impulse given by the impulse argument. A (steps + 1 x k_endog) array.

Return type:

array

Notes

Intercepts in the measurement and state equation are ignored when calculating impulse responses.