# Building A Model: Autoregressive?

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?

• what are the response values? Are they counts, categories, something else? – Glen_b Jul 17 at 3:36
• Hi, they're random numbers. – Eric CD Jul 17 at 3:44
• That's not conveying much. More context may help. – Glen_b Jul 17 at 5:52
• Is there some meaning to the ordering of the numbers as in is 1 closer to 2 than to 5, of are they arbitrary placeholders? – user3235916 Jul 17 at 7:29
• @user3235916 They're merely randomly generated numbers. – Eric CD Jul 17 at 10:16

The data ( 20 values ) and it's ACF suggests an AR(1) model (1,0,0) with Actual, Fit and Forecast here . The forecast for the next period is a "2" with 95 % limits being 0 and 3 using a monte carlo simulation.
The equation is here . I would appear that an auto-regressive model is sufficient.