How to improve this time series model? I am trying to fit a time series model for household data which is a time series variable.
Initially my data looks like this,

Since the data does not seem to be stationary I differenced the data. 
When I plot the 2nd difference data, it looks like follows:

The plots didn't improve when I took a higher order difference. So I used the 2nd difference data.
The acf and pacf of the 2nd order data are as follows,
 
To estimate the coefficients I used the yule walker method and following results obtained,
 
Then I tried the different combinations of models with 2 coefficients. I fitted ARIMA models for original data by considering the parameter for difference as 2(D=2). Using the AIC criteria, I got ARIMA (1,2,1) as the best model.
The model diagnostics results of this model as follows,


When considering the plots, it seems that the results are reasonable except the normality of residuals.
Can anyone suggest a way of improving this results? I am kind of new to time series so your advice will be a huge help for me.
The data set for this problem is follows,
I need to fit a model for the variable x4
Data set: 
 https://drive.google.com/file/d/1CXokm4p5ED2I03o0qGyWdxex38P-157M/view
 A: You politely asked "My question is about how to improve this model further . Because you will see that residuals are not normally distribute" . I have answered .....
I took your 290 monthly values (1987/1) and introduced them to AUTOBOX which automatically identified the following model.
1) ARIMA (1,1,0)(0,0,0)12  WITH AR COEFFICIENT=.865 THUS THIS IS VERY CLOSE TO SECOND DIFFERENCES WHICH YOU HAD CONSIDERED
2) 1 SEASONAL PULSE (POSITIVE) STARTING IN NOVEMBER 1996
3) 12 UNUSUAL VALUES (PULSES)
4) TWO MODEL ERROR VARIANCE CHANGES A) DOWNWARDS AT PERIOD 60 (1991/12) AND UPWARDS AT PERIOD 174 (2001/6) ... BOTH VISUALLY OBVIOUS FROM YOUR GRAPHS
This is the model 
The Actual,Fit and Forecast is here  with forecasts (and 95$ monte carlo based) here
The procedure following Tsay https://pdfs.semanticscholar.org/09c4/ba8dd3cc88289caf18d71e8985bdd11ad21c.pdf to identify variance change points yielded 
The model residuals are here 
The reasons that your software's attempt to model this data failed is that the original data is compromized by complications or opportunities.
