Hi all,

I've been looking through documentation to try to understand why Stata and
R occasionally come up with very different parameter estimates for ARIMA,
and am stumped. Existing discussion on this question, including code, can
be found here:
https://stackoverflow.com/questions/22443395/major-discrepancies-between-r-and-stata-for-arima.
I will summarize below for convenience.

Using historical Lynx Pelt data (
https://www.dropbox.com/s/v0h9oywa4pdjblu/Lynxpelt.csv), here are two
tables of AIC values from R and Stata for ARIMA(p,q) models for 0<=p<=5 and
0<=q<=5. Note that while most estimates match to seven significant digits,
several estimates diverge wildly, like the (1,3), (4,2) and the (3,2).

AIC calculations from STATA with technique(bfgs) for ARIMA(p,q):
           q0         q1         q2         q3         q4
p0  145.25614  100.20123   87.45929  77.570744  85.863777
p1  101.54848  84.916921   82.11809  86.444131  74.263937
p2  63.411671  49.424167  44.149023  40.966325  42.760294
p3  52.260723  49.196628  40.442078  43.498413  43.622292
p4  46.196192  48.195322  42.396986  42.289595          0

R results from above for easy comparison:

AIC calculations from R for ARIMA(p,q)
          q0        q1       q2       q3       q4
p0 145.25613 100.20123 87.45927 77.57073 85.86376
p1 101.54847  84.91691 82.11806 77.15318 74.26392
p2  63.41165  49.42414 44.14899 40.96787 44.33848
p3  52.26069  49.19660 52.00560 43.50156 45.17175
p4  46.19617  48.19530 49.50422 42.43198 45.71375


Note that I manually forced Stata to us BFGS as the optimization method to
match R, as the default usually alternates 5 steps BHHH and 10 steps BFGS.
In R, I turned off transformation of parameters & forced use of maximum
likelihood.

Do these differences result from starting values? The parameter estimates
(and acf/pacf) are sufficiently different in Stata & R that one could
logically arrive at different model specifications based solely on the
statistical program used.

Thank you for your help!

Twitter: @tbenst <https://twitter.com/tbenst>
LinkedIn: tylerbenster <http://www.linkedin.com/in/tylerbenster>

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