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Without using auto.arima, what are the ways we can figure out what parameters we should use for modeling a time series data ?

From the reference text here, it is mentioned that we cannot use correlation plots like ACF/PACF if the data is not satisfying couple of conditions.

If the data are from an ARIMA((p),(d),0) or ARIMA(0,(d),(q)) model, then the ACF and PACF plots can be helpful in determining the value of (p) or (q).16 If (p) and (q) are both positive, then the plots do not help in finding suitable values of (p) and (q).

Sample data that I am looking at. enter image description here

ACF of residuals after using a model with (0,1,3) (2,0,0) [12] fit enter image description here

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