Suppose a Markov chain with two discrete states $A$ and $B$. The probability of moving from $A$ to $B$ is $0.1$ and the probability of moving from $A$ to $A$ is $0.9$. Similarly, $B$ to $B$ has probability $0.9$ and $B$ to $A$ probability $0.1$.
Suppose the Markov chain describes a time-series where transitions from $A$ to $B$ and from $B$ to $A$ are something one would like to predict.
Given the current state, the best prediction of the next state is the most probable next state. With the described Markov chain, it would be the best to predict $A$ or $B$ constantly, depending on the where the process started.
This fails to be useful in predicting occurrences from $A$ to $B$ or vice versa, which is interesting. What should I conclude? That making predictions in such system is not possible? Or is the reasoning flawed with respect to
best prediction of the next state is the most probable next state
I asked the question https://stats.stackexchange.com/questions/168892/how-are-markov-chains-used-for-time-series-forecasting previously. This is related to that but not equal. Are Markov chain always not good for time-series prediction?