Timeline for Where do the error terms come from in ARMA?
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Apr 27, 2021 at 17:06 | comment | added | CBBAM | Sure I definitely will, I have written code for it over the past 2 days and have got it running but so far the results are not ideal (my predicted $\sigma$'s increase without bound during optimization. I am trying to debug, and if done successfully, I will post it. | |
| Apr 27, 2021 at 17:00 | comment | added | Richard Hardy | @CBBAM, I presume it is small when the sample size is medium to large. If you get around writing code for ARMA or ARMA-GARCH, it would be cool to see it. Consider posting it by answering one of your questions such as this one. I would appreciate if you pinged me then. Thank you. | |
| Apr 27, 2021 at 17:00 | comment | added | CBBAM | Thank you, how big of an affect does not optimizing $\epsilon_0$ have? | |
| Apr 27, 2021 at 16:59 | vote | accept | CBBAM | ||
| Apr 27, 2021 at 16:51 | comment | added | Richard Hardy | @CBBAM, yes, I think so. There are two caveats, though. First, this is conditional likelihood. In full likelihood, you would optimize for $\epsilon_0$, too. Second, naive optimization of the likelihood may be highly inefficient, take long time and fail to converge. (I think I tried it some years ago, and it did not go well.) Just look at the explicit expression of the likelihood in terms of the observed data and the parameters; the likelihood function is highly nonlinear w.r.t. the parameters, and that gets worse with sample size, if I remember correctly. | |
| Apr 27, 2021 at 6:23 | comment | added | CBBAM | Thank you! I have been doing some reading since I posted the question and it seems for an ARMA (1,1) process I would arbitrarily start with $\epsilon_0 = 0$ and recursively compute the sequence of $\epsilon_i$ through the ARMA equation, but rewritten as: $\epsilon_t = X_t - \mu - \theta X_{t-1} - \phi \epsilon_{t-1}$. With some assumed distribution, I take the maximum likelihood of these $\epsilon_t$ using the distribution's PDF. With $\mu$ being the mean of the data, I use this process to find $\theta$ and $\phi$. Am I on the right track? | |
| Apr 27, 2021 at 6:05 | comment | added | Richard Hardy | A starting point could be "ARIMA estimation by hand. | |
| Apr 27, 2021 at 6:02 | history | answered | Richard Hardy | CC BY-SA 4.0 |