Timeline for TimeSeriesModelFit incorrect?
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| May 16, 2015 at 10:51 | vote | accept | Skumin | ||
| May 10, 2015 at 11:50 | comment | added | Skumin | @JimBaldwin I don't really know whether Mathematica uses different methods... But it's probably the only possible explanation for the "differences in differences" of AICs. | |
| May 8, 2015 at 16:48 | comment | added | JimB | @Skumin. The ar function in R does give a difference of 0.041 when using the Yule-Walker method and 0.025 when using maximum likelihood. Might Mathematica's TimeSeriesModelFit be picking and choosing from different methods (although I don't see the options to pick Yule-Walker vs. maximum likelihood or the Burg method)? | |
| May 8, 2015 at 14:26 | comment | added | JimB | @Skumin. I concede you have a point. SAS and R both give 1.81 for that difference. And for AR(1) vs. AR(2) both SAS and R give 0.025 as the difference in AIC values while Mathematica gives 0.041. Also it does appear that the AR models leave off a different constant than for the GARCH models (which SAS and R do not do) and that makes it impossible to compare the fit between those two models using AIC. So maybe a bug report is justified. | |
| May 7, 2015 at 19:36 | comment | added | Skumin | Further (and possibly a slightly more relevant) comment: difference in AIC in Mathematica for ARMA(1,1) and ARMA(2,1) is 0.33, while the same difference is 1.81 in Stata and Gretl. | |
| May 7, 2015 at 18:21 | comment | added | Skumin |
Well, the thing is the documentation says that Akaike IS computed as $2k - 2\ln\left(L\right)$. Moreover, if I run TimeSeriesModelFit[data,"GARCH"], the optimal model from the GARCH family is GARCH(1,1) with AIC about 37000, i.e. the AIC is much higher than that of the AR(1) model - that is not surprising since Mathematica had selected the AR(1) over GARCH(1,1). But when I run GARCH(1,1) in Stata, I get lower AIC than that of AR(1) from Stata, i.e. according to Stata, I should prefer GARCH(1,1) to AR(1)...
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| May 7, 2015 at 18:02 | comment | added | Sasha | +1 Wholeheartedly agree. I was about to post an answer along this same lines. In Mathematica's implementation constants are dropped, therefore AIC differs from $2\left(k - \log\mathcal{L}\right)$. | |
| May 7, 2015 at 17:52 | history | answered | JimB | CC BY-SA 3.0 |