Suppose that I have a task of classifying a time series. I decide to use Hidden Markov Model $\lambda(A, B, \pi)$, where $A$ is a transition matrix, $B$ is an emission probability, $\pi$ is an initial distribution. An observed stochastic process looks as below
and there are two unobserved states: State 1 and State 2, also shown on the plot. Let's say, that I would like to fit HMM and test how it performs in terms of states recognition. The best thing I can probably do is to split my data into the train and test set but in a specific manner: the last $n$ observations make up my test set (the part to the right of the dotted green line), as I cannot use crossvalidation due to the temporal structure of the data. But there is a problem: to reliably assess the performance (measured as i.e. accuracy), I need at least a few transitions between the states that this data doesn't provide.
Question: is there any method that allows creating synthetic data for this kind of data? One thing I was considering was to reverse the whole training set, add some gaussian noise and tack on the end of the original training set.