Hi,

I need to test the hypothesis that fixed effects in my model do not correlate with deviations from the steady state from time 1 on in order to apply system GMM in xtaboond2 according to Roodman.
My data are panel and the variable under question is y:

Code:
* Example generated by -dataex-. To install: ssc install dataex
clear
input str4 atc3no float(Year y)
"A10D" 2004  22.15148
"A10D" 2005  22.30657
"A10D" 2006 22.425455
"A10D" 2007  22.54544
"A10D" 2008 22.711876
"A10D" 2009  22.90793
"A10D" 2010  23.09151
"A10D" 2011 23.213144
"A10D" 2012  23.32684
"A10D" 2013  23.54967
"A10E" 2004 17.460127
"A10E" 2005 15.233125
"A10E" 2006  13.80498
"A10E" 2007 17.687384
"A10E" 2008 17.763838
"A10E" 2009 17.642128
"A10E" 2010 17.612053
"A10E" 2011 17.626307
"A10E" 2012 17.678528
"A10E" 2013  17.67435
"A10H" 2004 20.555357
"A10H" 2005 20.438324
"A10H" 2006 19.775833
"A10H" 2007  19.49612
"A10H" 2008 19.285105
"A10H" 2009  19.17351
"A10H" 2010 19.319527
"A10H" 2011 19.522903
"A10H" 2012  19.43786
"A10H" 2013  19.34037
"A10X" 2004  15.09192
"A10X" 2005 16.236156
"A10X" 2006 17.594402
"A10X" 2007 17.977922
"A10X" 2008 18.303663
"A10X" 2009 18.415758
"A10X" 2010 18.589926
"A10X" 2011 18.681803
"A10X" 2012 18.646475
"A10X" 2013 18.569153
"A11A" 2004  22.54042
"A11A" 2005   21.5455
"A11A" 2006  21.54081
"A11A" 2007 21.640205
"A11A" 2008 21.760223
"A11A" 2009  22.01636
"A11A" 2010 21.985983
"A11A" 2011  22.03044
"A11A" 2012  21.97736
"A11A" 2013 21.984135
"A11B" 2004   20.8769
"A11B" 2005  20.46968
"A11B" 2006  20.29344
"A11B" 2007  20.16311
"A11B" 2008 19.688345
"A11B" 2009  20.09151
"A11B" 2010  19.72065
"A11B" 2011  19.45224
"A11B" 2012 19.596403
"A11B" 2013  19.68257
"A11E" 2004  19.52653
"A11E" 2005  18.55167
"A11E" 2006 18.251816
"A11E" 2007 18.072332
"A11E" 2008 18.030392
"A11E" 2009 18.399815
"A11E" 2010 18.860294
"A11E" 2011 18.501026
"A11E" 2012 18.439808
"A11E" 2013 18.047024
"A11F" 2004 16.994001
"A11F" 2005 16.907978
"A11F" 2006  16.86925
"A11F" 2007 17.033806
"A11F" 2008  17.27343
"A11F" 2009 17.641235
"A11F" 2010 17.882772
"A11F" 2011 18.076435
"A11F" 2012 18.098307
"A11F" 2013 18.349924
"A11G" 2004 17.647726
"A11G" 2005  14.97768
"A11G" 2006 14.476375
"A11G" 2007 14.556162
"A11G" 2008 14.447133
"A11G" 2009   14.4035
"A11G" 2010 14.234604
"A11G" 2011 14.745785
"A11G" 2012 14.802495
"A11G" 2013  14.72968
"A11X" 2004 18.248978
"A11X" 2005 17.706295
"A11X" 2006 17.597336
"A11X" 2007 17.427748
"A11X" 2008 17.384846
"A11X" 2009 18.027264
"A11X" 2010  18.85129
"A11X" 2011  18.77623
"A11X" 2012 16.929707
"A11X" 2013 16.825396
end
Now, as far as I have seen, I need to fit an ARIMA model for y. But then, how can I get the steady state value? Is it simply the mean of y? If so, over which time span?
Then how can I test for independence of fixed effects from deviations from steady state?

Thank you,

Federico