Modeling sleep patterns

My sleep is unpredictable. Not in a technical sense, but a colloquial one. To be literal, I have no idea how to predict my sleep. I just as often sleep through the day as I do through the night. My sleep itself, as far as a sleep study can tell, is normal. I can vaguely say, 60% confidence, if I’m likely to fall asleep in a given 3-4 hour period, and occasionally I will be fairly sure, 80% confidence, 6-10 hours beforehand, of a 1-2 hour period. I can similarly predict the length of my sleep (which is relatively normal—generally distributed 7, 8, 9.5, 13 hours at .1, .4, .6, .9).

My sleep is seriously disturbed. Without understanding the process behind my sleep, without being able to predict it days beforehand and understand the variables behind it, I find it impossible to wake up at a consistent time every day (+/​- 8 hours), despite years of trying, which makes it extremely hard to hold down a job, or do dozens of other normal things. There could be a profession that I could make my sleep work with, but I’m still searching for it.

So I ask you readers: Is there some sort of pattern detecting thing, whose name perhaps includes something like “markov” or “kolmogorov” or “bayesian”, that could automatically take a time series data and predict the next values based on an unknown, complex model?

So, I could like enter the times I go to sleep and wake up, and when I have caffeine or I exercise, and maybe other things, and it would puzzle out how my sleep works and forecast my next few sleep cycles?

To have an accurate tool like that would transform my life.

“Hidden Markov models” comes to mind, but at first glance I don’t see how a sleep model would count as a Markov process, given that you have to factor in sleep debt, time of day (because of sunlight), and perhaps other variables. But then I know nothing about HMMs.

Also, this is my first post. Is this the sort of thing that goes better in LessWrong or Less Wrong Discussion?