discovery about my sleep

[gusl]

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?

> summary(lm(ZQ~Time.in.Deep+Time.in.Light+Time.in.REM+Time.in.Wake, data=data))

Call:
lm(formula = ZQ ~ Time.in.Deep + Time.in.Light + Time.in.REM + 
    Time.in.Wake, data = data)

Residuals:
     Min       1Q   Median       3Q      Max 
-2.84975 -0.40340  0.02977  0.44843  1.54020 

Coefficients:
               Estimate Std. Error t value Pr(>|t|)    
(Intercept)   -1.100742   0.425614  -2.586   0.0113 *  
Time.in.Deep   0.356660   0.003818  93.417   <2e-16 ***
Time.in.Light  0.140365   0.001582  88.715   <2e-16 ***
Time.in.REM    0.211570   0.002877  73.549   <2e-16 ***
Time.in.Wake  -0.087905   0.003943 -22.292   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 0.8444 on 88 degrees of freedom
Multiple R-squared: 0.9983,    Adjusted R-squared: 0.9982 
F-statistic: 1.271e+04 on 4 and 88 DF,  p-value: < 2.2e-16