How to create confidence intervals based on simulations for ARIMA forecast

[Alejandra Rodriguez-Morales]

Hi, I am trying to make a forecast in Stata15 using an ARIMA model. My data is as follows and goes from 2003m1 to 2019m12:

date x_lithium
1/1/2003 3.2596932
2/1/2003 3.7835287
3/1/2003 7.8802617
4/1/2003 5.3377245
5/1/2003 5.1322163
6/1/2003 5.1343488
7/1/2003 6.6340138
8/1/2003 6.8402285
9/1/2003 4.0908843
10/1/2003 6.7880796
11/1/2003 4.6890101
12/1/2003 5.2351787
1/1/2004 4.572536
2/1/2004 5.5246196
3/1/2004 6.2288512
4/1/2004 5.5700383
5/1/2004 6.0764194
6/1/2004 5.4765314
7/1/2004 7.8750602
8/1/2004 7.1462818
9/1/2004 6.1501641
10/1/2004 5.5155473
11/1/2004 7.9347098
12/1/2004 7.10945
... ...

I have managed to make the prediction using an ARIMA model (I think everything is correct).

generate t=tm(2003m1)+_n-1
format t %tm
tsset t
tsappend, add(60)
twoway (tsline x_lithium)
ac x_lithium
pac x_lithium
arima x_lithium, arima(2,0,1)
estat ic
predict cp
predict cp_dynhat, dyn(2030)
tsline x_lithium cp_dynhat

My result:

But I don't know how to calculate the confidence intervals based on simulations for my prediction and display them on the graph.

Thank you in advance!