Suppose $\{X_n\}$ is the hidden Markov chain, and $\{Y_n\}$ is the series of observations, where $\mathbb{P}\{Y_n = j| X_n = i\}$ is the same for all $n$ (please correct me if I have not stated the definition of hidden Markov models correctly). How does one show rigorously that $\{Y_n\}$ does not have the Markov property?
Thank you in advance.