The control chart from the momentum center: https://gamma-trader.shinyapps.io/center/ displays a lot of useful statistical information. Things like Skew, Kurtosis, Mean, Standard Deviation, Realized Volatility. I pay attention to all of them and each provides useful information, but the one that I'm always looking at other than realized volatility is Kurtosis. Those of you with a STEM background might already know what Kurtosis is and what it measures but I want to expand on the way I interpret the value in the context of intra-day log returns from the market.
Kurtosis provides a measure of the number of outliers in the distributions (green dots and red dots in the chart). For a normal distribution (Gaussian) kurtosis is exactly 3.0 and that is my reference point in the control chart. Most days we get values very close to 3.0 (for instance right now we are getting 2.43) when that happens it means that the market is just drifting randomly in an almost pure Brownian motion (like pollen floating on a glass of water). This is a sign that market participants have a general agreement about price levels and that is why the drift is small. When kurtosis starts to deviate from 3.0 in a big way (8, 9, 10 or higher) then it means that there is no good price agreement and that market participants are incorporating new information into the market, which could be a great piece of information into itself.