I have a repeating sequence like the following, with occasionally random values (maybe noise): ABCDABCEDABCDABCD
What could be an algorithm to model the sequence and predict a following value at a certain time. For example I had ABC and no it should say D (of course it can only give a percentage since it is not always D following ABC).
First I wanted to try HMMs, but I think there is no hidden state, since i ABC are my states and can be observed. My second thought would be markov chains, but I am not quite sure if there is an good way to learn the probabilities and give me a prediction given one or two (for a second degree markov model) of the following value.
I also wanted to look into RNNs, but it would be great if someone with experience could tell me in advance if they are a good way for this task or if I should focus on more promising ways.