Timeline for Show that $Y_t$ and $Y_{t+h}$ are independent if $X_t$ is Gaussian
Current License: CC BY-SA 4.0
4 events
when toggle format | what | by | license | comment | |
---|---|---|---|---|---|
Apr 23, 2021 at 13:27 | comment | added | mark leeds | Parseval: Even with the independence assumption, you still need the $h > q$ assumption, Otherwise, if $h$ was not necessarily greater than $q$ as steveoamerica pointed, you would have some terms that were the same in the two $Y_t$ and $Y_{t+h}$ which makes $Y_t$ and $Y_{t+h}$ "dependent" because they contain some of the same terms. But, "dependent" is maybe a misleading term in that case. It's more like "common term" dependent. | |
Apr 23, 2021 at 13:20 | comment | added | mark leeds | He did add later than it was an MA(q) so all the $X_{t}$ are independent. I like your proof with the block diagonal argument. It's more "visual" than ugly algebra. | |
Apr 22, 2021 at 20:26 | comment | added | steveo'america | We need not require all $X_t$ be independent, of course, only that the first $q+1$ elements of $\vec{X}$ be independent of the second $q+1$ elements, which would make $\Sigma$ block diagonal (2x2). | |
Apr 22, 2021 at 19:42 | history | answered | steveo'america | CC BY-SA 4.0 |