Fan Chart (Predictive Density) - Forecast from a State-Space

[jpfeifer]

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IRFs from the ABCD state space representation

Matlab’s state space uses y_t=\tilde Cx_t+\tilde D\varepsilon_t , but Dynare’s ABCD form reports y_t=Cx_{t-1}+D\varepsilon_t. With x_t=Ax_{t-1}+B\varepsilon_t you get y_t=(\tilde CA) x_{t-1}+(\tilde CB+\tilde D)\varepsilon_t. Comparing coefficients, you should get \tilde C=CA^{-1} \tilde D=D-\tilde C B However, that requires A to be invertible, which it is often not.