discovery about my sleep

I just made a big discovery from my sleep dataset (93 nights): my "Time in REM sleep" has a strong autocorrelation, i.e. I have streaks of high REM sleep nights, and low REM sleep nights.

Here are some statistics, 1-day auto-correlations for different quantities:

	rho-hat	CI	p-value
Total Sleep time		[-0.213, 0.197]
ZQ	0.22	[0.0114, 0.4028]	3.8e-02
Time in Deep	0.29	[0.0915, 0.4678]	4.9e-03
Time in REM	0.43	[0.247, 0.584]	1.87e-05
Time in Light		[-0.243, 0.166]

The data also suggests that 'Time in Deep' has a significant autocorrelation, but not as strong as 'Time in REM'.

Here's a time series of 'Time in REM':

In the above plot, we see that I had a streak of 6 days in my top quartile, and a streak of 7 days in my bottom quartile... which would be unlikely without autocorrelation.

For comparison, see a series of 'Total sleep' (the really bad nights correspond to a nasty strep infection I had earlier this year):

The natural scientific question is: what factors predict (or better, cause) periods of high REM sleep?  I've computed a tiredness variable, as an exponential moving average of 'Total Sleep Time' (or 'ZQ'), and it suggests that the more tired I am, the less REM sleep I will have... but this effect is estimated at 0.216, which is more modest than the autocorrelation in REM Sleep, so it could be due to confounding (i.e. I am most tired when my previous night's REM Sleep was low, which predicts the next night's REM Sleep also being low).

Note that ZQ is defined as a linear combination of the different phases of sleep, so it's not all that surprising that it seems to have some degree of autocorrelation.  If Z=X+Y, can we decompose autocorrelation(Z) into components?

( Read more... )