Statistic to describe variability of a time series value This statistics newbie could use some help with time series statistics.
I am looking at sunlight (irradiance) over the course of a day. One day got cloudy, so the values went down, mid-afternoon. The curve looks like this:

The next day, was clear, so the curve has only 1 clear apex:

Is there a statistic to describe each day as "steady" or "changeable"?
 A: You could evaluate the Energy spectral density integrated over a range of frequencies which you consider relevant to your idea of variability of irradiance .  The energy spectral density is the squared absolute value of the Fourier transform of your time-series measurement (in your case, irradiance). If you integrated over frequencies between (say) 10 times per day and 100 times per day then a day with a sunny morning and cloudy afternoon would have a low variability but a day with the same level of change happening half-hourly would have a high variability.
A: I'd start with looking at the roughness type of metric, e.g. the sum of squared second differences $$\sum_i (x_i-2*x_{i-1}+x_{i-2})^2$$ or the variance of these differences.
A: Suppose you use only data from sunrise to sunset.  With no obstruction, it appears that a quadratic trend in time adequately models your data.  When an obstruction occurs, the quadratic fit would be less adequate.  Hence, one can test the discrepancy between the quadratic fit and a nonparametric fit (LOESS, local linear regression, etc.) to a dataset.  Perhaps simpler, one could test the linear model vs the quadratic model.  If the quadratic fit does not hold, then obstruction has been detected and you can mark it as "changeable."
