Seems you're trying to segment based on volatility and trend which might be two different/separate problems. Googling 'change point detection' might be a good start (or see https://arxiv.org/abs/2003.06222). There are tests which test for both changes in location and scale (i.e. trend and vol).
The Open and the Close will be consistent timing and will be valid.
The High and Low of each instrument will not be time consistent. In particular it will be especially erroneous to divide the appl(H) by amzn(L) to get the highest ratio or the appl(L) by amzn(H).
The likelihood that both prices were at the highs at similar times and the lows at similar times ...