Timeline for ARIMAX: only MA(1) model gives meaningful coefficients for exogenous variables
Current License: CC BY-SA 4.0
20 events
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| Jun 4 at 4:19 | comment | added | mlofton | This is the baltagi text I'm referring to. He has a few different ones. link.springer.com/book/10.1007/978-3-030-80149-6 | |
| Jun 4 at 4:00 | comment | added | mlofton | if you can't get your hands on harvey, another book that doesn't do a bad job with ARDL's, the koyck distributed lag and partial adjustment is Baltagi. But there's not better book than Harvey in my opinion. | |
| Jun 3 at 17:21 | comment | added | mlofton | If you have any questions after going through what I suggested, feel free to ask back here. I think what you're doing is interesting and the plots you made show that you know what you're doing. | |
| Jun 3 at 17:19 | comment | added | mlofton | Hi Arthur: I'm not sure if I implied it but I DEFINITELY did not mean to imply that you should use OLS. That won't work because it's not dynamic. You need a dynamic model ( t subscripts ) that has an error term that leads to a partial adjustment model. If you read about dynamic models and partial adjustment in Harvey's book, you'll see more what I'm referring to. It's difficult to explain a whole book ( well really a couple of chapters called. They are dynamic models I and II IIRC ) in a comment. But I suggest that you not just jump to those chapters and read the book from the beginning. | |
| Jun 3 at 17:08 | comment | added | Arthur | @mlofton I agree that doing OLS on the data is very straightforward and could produce adequate coefficients in many cases. But what about systems where the exogenous variables are constantly changing and the system is almost always in a dynamic state? A model without any dynamics would treat this all as error. The quality of fit would be poor, and the residuals would be autocorrelated. | |
| Jun 3 at 17:02 | history | edited | Arthur | CC BY-SA 4.0 |
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| Jun 3 at 16:01 | history | edited | Arthur | CC BY-SA 4.0 |
more elaboration on the bagel
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| Jun 3 at 15:58 | comment | added | Arthur | I edited my post with language "regression with ARIMA errors" and with elaboration of the bagel example. The data and plots should reflect more intuitively the dynamic heating of the bagel. | |
| Jun 3 at 15:55 | history | edited | Arthur | CC BY-SA 4.0 |
more elaboration on the bagel
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| Jun 3 at 15:30 | comment | added | mlofton | This what I'm referring to. I had the title wrong. It's not terribly popular and it's old but very under-rated. Harvey is not easy to read because he has a very terse style but if you keep your nose in it, you can get a lot of out of it. Andrew Harvey: "Econometric Analysis of Time Series". It's on amazon for around 70.00. | |
| Jun 3 at 15:30 | comment | added | Arthur | I think I understand. Is it just that I am using the term "ARIMAX" incorrectly? | |
| Jun 3 at 15:28 | comment | added | Stephan Kolassa |
Rob Hyndman (the author of that blog post) is the maintainer of both the forecast and the fable packages and explicitly notes at the very bottom of the post that he implemented regression with ARIMA errors, not textbook ARIMAX. And what "the right way" is is quite open to discussion...
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| Jun 3 at 15:23 | comment | added | mlofton | Note that, in any standard time-series econometrics text, you;ll find material on the ARDL and particularly the koyck distributed lag ( this is related to what you're doing indirectly ) but I still recommend Harvey above. It's better than the standard treatment in those books. | |
| Jun 3 at 15:17 | comment | added | mlofton | Hi: It's an interesting thing that you're trying to model and too complex for me to say anything terribly useful ( without working on it myself and even then who knows ). But I see one issue. Don't make them exogenous regressors to an arima model. Those variables ARE the variables of the model. So, they can be exogenous but not to ARIMA model. I would DEFINITELY check out Harvey's "econometric time series analysis" and particularly partial adjustment models. It's really the only book ( atleast statistics-econometrics related ) that I know of that talks in depth about these type of problems. | |
| Jun 3 at 15:15 | comment | added | Arthur |
Because I am using auto.arima and Arima from the forecast package, I believe that I am fitting the models "the right way" and thus my question is unrelated to that blog post. My question is more about "what is the relationship between (time series models with exogenous regressions) and (ODE models)?" and less about the different flavors of ARIMAX. Admittedly, I am a pure practitioner, and my theory is weak.
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| Jun 3 at 15:01 | comment | added | Stephan Kolassa | I unfortunately can't follow all of your argument. But it may be helpful to consider that ARIMAX is not the same as ARIMAX, or to be more precise, standard auto-ARIMA software fits a regression on the predictors plus an ARIMA model on the residuals, not textbook ARIMAX, see robjhyndman.com/hyndsight/arimax. So since the regression is done before its residuals are modeled using ARIMA, it seems like your title question would not make sense in this model. | |
| Jun 3 at 14:26 | history | edited | Arthur | CC BY-SA 4.0 |
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| Jun 3 at 14:19 | history | edited | Arthur | CC BY-SA 4.0 |
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| Jun 3 at 14:14 | comment | added | Arthur | Thank you, Steven, but I don't think that link covers my question. | |
| Jun 3 at 14:09 | history | asked | Arthur | CC BY-SA 4.0 |