In the literature I read that the observation $\epsilon_n$ depends both on the hidden process $\Delta_n$ and the lagged observations $\epsilon_{n−1}$, it is called Markov Switching Model. So graphically I built up this representation which shows the relationship.

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However in the application some papers when they condition $\epsilon_n$ on past observations they do not condition on only the previous observation $\epsilon_{n-1}$ but the whole past observed process. Am I confusing some part of the dependence structure?


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