How choose a proper ARIMA model? I am doing my project on forecasting and I have to use the ARIMA for it.
I have tried but still unable to identify which ARIMA model is appropriate for my data set?
Either to use ARIMA or SARIMA.
Here is the ACF:

And the PACF:  
 A: In general the model building process is here https://autobox.com/pdfs/ARIMA%20FLOW%20CHART.pdf . In specific here is the actual data (99 monthly values)  . The acf of the original data is here  
After seasonal differencing the acf/pcf is here 
suggesting the following model 
As part of the model identification process we use the CHOW test to test the hypothesis that the model parameters are invariant over time. Not so in this case … and decidedly not so visually . suggesting a partitioning of the data at or about period 58 thus 1-57 has been found to differ from 58-99 . This apect of modelling is often ( if not always !) overlooked in modelling chronological data but I find is quite prevalent in data.
This specific form of non-stationarity in the data would probably cause havoc AND confusion with simple AIC based model detection algorithms .
Analyzing the most recent 42 values  we find the following model.  suggesting a pulse at the last point .
The residuals from this model have an acf suggesting sufficiency  and plotted here 
The plot of the Actual/Fit and Forecast from this tour de force is here  showing forecasts for the next 36 periods on the premis that the actual value at the ultimate data point is a pulse (one-time aberration)
I show here the result of 1000 simultions the probability density function for the forecast interval for 1 period out via bootstrapping 
THis was all done AUTOMATICALLY using AUTOBOX wich I have helped to develop.

