A colleague sent me the following information regarding this question:
Actually the documentation does mention that a time-varying measurement matrix, H_t, is permitted. All you need to do is provide H_t that is a ((T+lead)*N_y) times N_z matrix where, T is the number of time points, lead is the forecast lead, N_y is the dimension of the observation vector, and N_z is the dimension of the state vector. For example, in the user’s notation, if the observations are univariate, the rows of H_t matrix will be [1 M_t], t=1 …(T +lead).
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