Finding unpredictability or uncertainty in a time series
Since you have looked at Kolmogorov-Smirnov and Shannon entropy measures, I would like to suggest some other hopefully relevant options. First of all, you could take a look at the so-called approximate entropy $ApEn$. Other potential statistics include block entropy, T-complexity (T-entropy) as well as Tsallis entropy: http://members.noa.gr/anastasi/papers/B29.pdf

In addition to the above-mentioned potential measures, I would like to suggest to have a look at available statistics in Bayesian inference-based model of stochastic volatility in time series, implemented in R package stochvol: http://cran.r-project.org/web/packages/stochvol (see detailed vignette). Such statistics of uncertainty include overall level of volatility $\mu$, persistence $\phi$ and volatility of volatility $\sigma$: http://simpsonm.public.iastate.edu/BlogPosts/btcvol/KastnerFruwhirthSchnatterASISstochvol.pdf. A comprehensive example of using stochastic volatility model approach and stochvol package can be found in the excellent blog post "Exactly how volatile is bitcoin?" by Matt Simpson.