Timeline for Infinite-variance associated processes are (BL, $\theta$)-dependent
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 2, 2022 at 7:25 | vote | accept | AlbertRapp | ||
| Nov 2, 2022 at 7:25 | comment | added | AlbertRapp | Oh I see. I understand your comment now. I'll create a follow-up question about associated alpha-stable moving averages. This is really the main process I'm interested in but I thought maybe the it could be answered in more generality. | |
| Nov 1, 2022 at 20:05 | comment | added | Iosif Pinelis | @AlbertRapp : I don't see such an implication. My answer only deals with "degenerate" processes -- constant in $t$. As for my previous comment, it only says that, if the desired property were true for all non-degenerate processes (with infinite variance), then it would hold for all processes with infinite variance -- which latter is false, by my answer. So, my comment only implies that the desired property is false for some non-degenerate process. | |
| Nov 1, 2022 at 18:54 | comment | added | AlbertRapp | I'm still a bit hung up about this. Wouldn't your solution imply that no infinite-variance process can be (BL, $\theta$)-dependent? This does not sound right. Where is my error? | |
| Oct 31, 2022 at 19:00 | comment | added | Iosif Pinelis | @AlbertRapp : You can approximate a degenerate process $X$ by non-degenerate ones however well, in terms of this setting. So, if we had your desired property for all non-degenerate processes, we would also have it for the degenerate ones, which is impossible, as shown in the answer. So, the non-degeneracy condition will not help. | |
| Oct 31, 2022 at 18:50 | comment | added | AlbertRapp | That's a very elegant counterexample. I should have thought of that and made my question more precise. What if $X$ is non-degenerate, e.g. alpha-stable? Is there any way to bound the covariance then? | |
| Oct 31, 2022 at 17:18 | history | answered | Iosif Pinelis | CC BY-SA 4.0 |