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

Impulse response function

stepsint, 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.

impulseint 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).

orthogonalizedbool, optional

Whether or not to perform impulse using orthogonalized innovations. Note that this will also affect custum impulse vectors. Default is False.

cumulativebool, optional

Whether or not to return cumulative impulse responses. Default is False.


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


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

TODO: add note about how for time-varying systems this is - perhaps counter-intuitively - returning the impulse response within the given model (i.e. starting at period 0 defined by the model) and it is not doing impulse responses after the end of the model. To compute impulse responses from arbitrary time points, it is necessary to clone a new model with the appropriate system matrices.

Last update: Jul 16, 2024