Edit: I've written up a C program to do some brute force calculations on some of the shiny odds. Here's what I've found so far:
Shiny correlations to the Trainer ID
DO EXIST, but they're miniscule. The worst "shiny ID" is 5185, with odds 523936 in 4294967296, or
0.9993 in 8192. The best shiny ID is 586, with odds 524620 in 4294967296, or
1.0006 in 8192.
These figures are created assuming that the game draws two successive random numbers, one for the lower 16 bits of the PV, the other for the upper 16 bits. I calculate "shiny ID," the portion of the trainer IDs that matters for the shiny calculations, by XORing the Trainer ID with the Hidden ID, then bitshifting the result down by 3 bits, yielding some value between 0 and 8191 inclusively.
These calculations don't consider the effects of things like Synchronize/Everstone. I'd repeat my calculations if I knew how they calculate PVs for Everstone breeding and such, but I don't, and I can see a multitude of ways they could have written them which would work.
Since 8192 and 25 are
relatively prime, I don't expect to see any significant ID correlations there either.
When I did only a partial trial for a smaller range of PVs (the complete calculations take several minutes on my Athlon64 3000+), I got some shiny IDs which didn't yield any shinies, however. I shall try to see just how long the longest "drought" can last on any ID. This is going to be of interest for Emerald SRing, but not much else.
Edit2: Repeating the calculations using a theoretical model for Bold natures w/Everstone.
Edit3: Under my purely hypothetical Everstone/Synchro model, with Bold nature, the worst SID is 8127 with odds 491466 in 4294967296 (0.9374 in 8192--seems low but is still just 1 in 8739), and the best is 8191 with odds 573440 in 4294967296 (1.0938 in 8192). I will now repeat the trial with my Emerald's shiny ID--7277.
Edit4: My results for my Emerald ID: There are 524732 Bold shinies in the mix, so the odds are just slightly above average at 1.0008 in 8192. The longest drought in the stream lasts 102332 values (thank GOD those aren't SRs! D=), which corresponds to about a half hour of gameplay. This half hour of gameplay could be placed anywhere in the 828 CONSECUTIVE DAYS it takes for the RNG to repeat itself. It's very likely that there are other such long droughts, however. The shortest drought was 1 value, meaning that somewhere in there (or in multiple spots), there are two consecutive shinies.
So, to summarize (without techno sp33k), looks like my Emerald isn't cursed after all. All I need to do is keep on going, being sure to leave my game turned on for a random number of hours, and I might get my shiny.