I am quite lost about the use of time scaling to estimate volatility. It is said that “Square root of time scaling assumes independent price moves (no autocorrelation) and constant volatility”, so that means the prices follow a random walk.

a random walk always looks a trending market to me, but a trending market implies autocorrelation and will render the time scaling/square root of time rule inaccurate. how to differentiate a trending market from a random walk if they both seem to be trending…?