I've recently read a code about a fisheries productivity model where someone tries to predict the value at time t+1 from its value at time t. There're 23 recorded productivity of tuna from 1967 to 1989, and try to predict the productivity in 1990. An autoregressive model was build and the prediction was done using Markov Chain Monte Carlo method.
I'm wondering if i can use the same approach to solve my problem. I want to be able to predict the next state based on the previous state(s). There are 5 possible states, random numbers 1, 2, 3, 4 and 5.
I have data and it looked like this
.......1, 4, 2, 5, 1, 4, 1, 2, 5, 3, 4, 1, 4, 3, 3, 2, 4, 2, 2, 5.
I'd like to predict the next value after the last '5'. Is it possible to do this with the same approach in the Fisheries Productivity Model (Autoregressive Model + MCMC)?
Otherwise, which model is more appropriate?