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I tried to fit time series model. Below is the plot of my original series by tsdisplay(mydata_ts).

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I think it's quite clear that there is no trend but only seasonality in this series. So, I did 12 lags diff and this resulted in the following ACF and PACF below.

enter image description here

enter image description here

It seems that ACF and PACF lost the effect of seasonality. The confusion is should I include the seasonality effect in my SARIMA(6,0,5)(0,1,0)12 or should I simply use ARIMA(6,0,5)? Then again does ARIMA(6,0,5) seem to be too complex to use AR(6) and MA(5)? Any thought will be appreciated.

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I would say that both the options are the same . You should not even see any coeficients for the seasonal part in the Sarima model part of the model with both P, Q = 0 . You can also compare the two models using AIC or BIC on a test data set to be sure .

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