This is a good paper introducing categorical time series analysis:
https://projecteuclid.org/download/pdf_1/euclid.ss/1076102425
This is a good paper introducing categorical time series analysis:
https://projecteuclid.org/download/pdf_1/euclid.ss/1076102425
Hi, the paper suggested by Ayman Amin is extremely interesting. Yet, once we have the conditional distribution of the cathegorical variable it is not entirely clear how to build a reasonable forecast.
In the case of a balanced dice, let us assume that the unconditional and conditional distribution is 1/6 for each outcome. We know that the forecast that minimizes the Mean Squared Error is the conditional expectation, which is equivalent in this case to the unconditional expectation, which is 3.5=(1+2+3+4+5+6)/6.
Yet how useful is 3.5 as a forecast for the results of rolling a dice? I think it is quite useless. So the choice of a correct function to generate the forecast is also something to address. Natural candidates are: the outcome with the highest conditional probability, or the outcome closest to the conditional expectation. I am not sure which one will perform the best in practice though. Hope it helps!!
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