"Can I use multinomial logistic regression for predicting the target variable which is categorical which more than 2 levels "
Answer is yes. That lead to General Logistic Model.
An alternative method is using Decision Tree which Data Scientist love it . But you need SAS/EM to run it.
"so I want to predict the on the future data. and also there could seasonality effect inside the data."
Do you mean these data are Time Series data ? then you need SAS/ETS .
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