Timeline for What subset of ARMA(1,1) processes can be represented as AR(1) - a query about the logic in this derivation
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Nov 27, 2020 at 14:17 | comment | added | hydrologist | In trying to answer the AR(1) + AR(1) question, I need to answer the MA(1) + MA(1) question, which in turn requires constraints for the MA(1) = MA(1) = white noise case. I have created a new post outlining my tentative progress on this here: stats.stackexchange.com/questions/498300/… | |
| Nov 25, 2020 at 14:23 | comment | added | hydrologist | Thanks Jarle. I have been trying to do this, but got rather stuck. Having re-read your answer I think this might be because, in order to show how ARMA(2,1) could be AR(1) + AR(1), I also have to show how MA(1) could be MA(1) + MA(1). I will investigate and post further... | |
| Nov 25, 2020 at 11:45 | history | edited | Jarle Tufto | CC BY-SA 4.0 |
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| Nov 25, 2020 at 9:56 | comment | added | Jarle Tufto | In much the same way. Again you get two right hand sides that are MA(1) that need to have the same autocovariance functions for the representations to be equal. This gives you two equations that you can solve for the white noise variances of the two AR(1) processes and these variances need to be non-negative. In addition, the roots of the AR(2) polynomial needs to be real, such that each AR(1) process has real coefficients. | |
| Nov 24, 2020 at 23:21 | comment | added | hydrologist | Great answer! How would one go about a similar argument to find the subset of ARMA(2,1) that could be represented by AR(1) + AR(1) ? | |
| Nov 24, 2020 at 14:26 | vote | accept | hydrologist | ||
| Nov 24, 2020 at 12:34 | history | answered | Jarle Tufto | CC BY-SA 4.0 |