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I have data which can take discrete values (between 0 and 5). I have 2 values per day during 2 years which contain a lot of 0 and 5. I know that my data are correlated with end of week, end of month, end of semester... I also know that in the data there is an X weeks seasonality. This X period is susceptible to change through time. It is even possible that I have in my data at the same time an X and a Y period in my data.

This is the shape of my data. 11 is the fifth value:

enter image description here

I have tried ARIMA, the shape is good but as it is ARIMA I can not manage to get discrete values and the mean is not really relevant in my data.

I was looking into the question below since my issue is very similar. However, I think that HMM is not very suited for my problem mostly because of the multiple seasonalities.

Problem in discrete valued time series forecasting

I am starting in this field and I do not have a strong stastistical background. What should I use to be able to forecast a value ?

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    $\begingroup$ Looks like a place for a Bayesian hierarchical mixed effects model for an ordinal outcome. See for example the R brms package. $\endgroup$
    – Frank Harrell
    Commented May 29, 2018 at 12:02

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