According to my theory when we are seeing rapid fluctuations in price it means that there is soon to be a sudden jump to the new state.
The more fundamental problem is that the oscillation damps out after the step. What you are showing is the opposite of what you are describing. Reverse the arrow of time on your graph and you would be showing what you are describing. Perhaps Mig could find an anology in quantum theory for such a scheme. It is far beyond me, but I did spend a lot of time looking at deformed square waves when I was designing audio circuits back in the 70s. As the Dutch said while fighting the Spanish: "It is not necessary to have hope in order to persevere."
To me, the noise is the signal in financial price series, and if you stripped it out you'd be left with the naked square wave. Most economists teach a theoretical framework that has been shown to be fundamentally useless. -- James K. Galbraith
Real economies are based on politics, not maths. You can't design signal flows until you specify social outcomes, and the big problem we have at the moment - and have had for decades now - is that the people who design the outcomes have been utterly dishonest and manipulative about what they've been trying to achieve.
At best they've been dishonest with themselves, and at worst they've simply been acting criminally.
If you want to model the economy accurately, you don't need square waves, you need special prosecutors.
