Leading and trailing extremes

This was one of the things that just bugged me to the point where I needed to actually sit down and figure it out. Here is the complete picture:
The data is pretty straight forward, recording 2 extremes (high/low) within each “hour” and storing them into a 10 minute bin. The question is: Why does the area where the extremes are vary so much from hour to hour? Personally, I had a hard time seeing the relationship and working it out in my head until I had all of the sets complete. Can you see a pattern?

When I think about extremes, I think about what I call the leading extreme, which is more or less the same as the “trend direction”. Take the following snapshot, where i’ve deleted the time stamps so that we can make them up.
Let’s assume that we are looking at a typical case where the yellow lines are representing xx:00; That is, 33% of the time an extreme is located in the last 10 minutes of the hour. The yellow circle is representing that the extreme is indeed in the last 10 minutes. Great!  Now if you imagine the vertical yellow lines shifting over 10 minutes, now starting at xx:10, we can see that price dips down, and the high extreme is still located at that peak, which is some time between xx:50 and xx:00. So why is the probability 33% in some cases and as low as 12% in others?

Because of the trailing extreme. Let’s take a look at a side by side:
Again, assume the times of the first extremes to be xx:00-xx:10 and xx:50-xx:00 as shown by the yellow circles. Now if we shift the time forward by 10 minutes, the extremes are now xx:10-xx:20 and xx:50-xx:00. The “leading” extreme time has not changed, but the first extreme (the low) has now been shifted 10 minutes forward.

This means that when price is like above, in a healthy/strong trend, or occurring in an area where price moves in one direction only for a period of over 10 minutes, it creates a varying extreme on one end, even if the other end (the high in this case) remains the same.

The big question now: Does it matter? Maybe.
I mean it’s not completely insignificant. The biggest probabilities within each set are not that small, at least twice as big as the ones that are least likely. If you take the two largest probabilities in each set (which are always next to each other), the number ends up being close to or over 50%. That is, no matter what time you use as your start time, a particular 20 minute period will contain an extreme 50% of the time. That is, 33% of time will contain 50% of extremes. That’s pretty cool!

With this understanding, the relationship is a bit clearer now. Given how the trailing extreme functions, The higher probability numbers are occurring where we expect them to be: 10 minutes trailing.. for the most part.
There’s something that sticks out very clearly, and that’s the pause that happens from the xx:30 start to the xx:40 start. Remember that the binned number is the max. This means that for both those periods, the minutes of xx:20-xx:29 contain an extreme more often than any other 10 minute chunk. Therefore, the stats seem to favor the xx:20-xx:29 period as the best period to be making extremes of all time frames by a slight margin.


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