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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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With a slight tweak to the modelling heuristic in AUTOBOX, here is the ACF of the (new) model's errors enter image description here

The model is here enter image description here and here enter image description here with a refined (two change points) variance change test enter image description here

The Actual/Fit and Forecast is here enter image description here and statistical summary here enter image description here

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  • $\begingroup$ From the AutoBox output how do we know what the parameters are ? I am not sure how to intepret the equations that you have there $\endgroup$ – statlearner Jun 13 at 5:48
  • $\begingroup$ using the most recent model (3,0,0)(1,0,0)12 omitting the second lag in the regular ar polynomial. The simple pdq notation is insufficient to explain the fact that there is a ar polynomial with 2 coefficients lag 1 and 3 . Does this help you.? with 3 pulses and 1 level shift $\endgroup$ – IrishStat Jun 13 at 6:01

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