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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