bar(n)-bar(n-1): anyone recognize this curve?

Z

zedDoubleNaught

When I take the difference between one value (price, volume, anything) and its previous value, then sort them ascending, I always get a curve that looks like the attached. It looks like a very wide, flat tangent curve; or, it starts very negative, rises sharply, then a flat mildly positive sloping line, then rises sharply at the end. Just wondering if anyone recognizes it and knows any research or work on it they could point me to. Thanks in advance !!

I think it could just be another way of drawing out a distribution, where most of the values are around an average and has a few large outlier values. I don't know if it means anything, but seems to be fairly consistent.
 
trying to repost image:

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each curve is 112 bars, of the difference between one bar's close and the previous, which is about one week. There are curves from 10 weeks, taken at random between June 2010 and Jan 2011, being careful to avoid weeks with holidays in them. The curve with the big yellow triangles is an average, that's why it's very smooth.
 

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Thanks dave4532 for the link, this is the type of thing to study I was looking for.

darkcanuck -
Here are the histograms, looks like they are trying to approach bellish curves. It's got the histogram of all the data from the 10 non-contiguous (or non-continuous) weeks of 1100 values, and the second one is the histogram of the average set with 110 values. The average is not so smooth, presumably because it only has 100 values.

I'm not surprised, I've found most histograms come out looking bellish. "Bellish" because I've seen on other threads that a data set of 100 or 1100 is probably not enough to be meaningful, and people disagree about what kind of bell it is. I'll stick with "bellish" as simply meaning: there's more in the middle than at the ends.

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For the original swooping curve, I got this formula from eureqa:

0.001402044*tan(0.023389222*index - 1.3131371)

My guess is this means it is a tangent, stretched out to extend across my 110 values, and a couple of numbers to adjust the left-right and up-down shift to fit my values. There were other formulas, but I've chosen this one to follow up on until disproving it because it fits my first impression.

(the attachment is the same jpg as the posted screenshot)
 

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Quote from zedDoubleNaught:
----a curve that looks like....
----It looks like a....
----wondering if anyone recognizes it....
----any research or work on it they could point me to.
----another way of drawing out a distribution....
----large outlier values.
----seems to be fairly consistent.
More...
1) The outliers may conform to some type of power-square law. :confused:
2) The curve can denote "balanced randomness". :eek:
3) If you do the same with the profit & loss from each trade you make, it ought to look similar. :)
4) You want to be sure to eliminate the outliers all the way to the left-side. :D
 
Quote from zedDoubleNaught:

Here are the histograms, looks like they are trying to approach bellish curves.

...

For the original swooping curve, I got this formula from eureqa:

0.001402044*tan(0.023389222*index - 1.3131371)

My guess is this means it is a tangent, stretched out to extend across my 110 values, and a couple of numbers to adjust the left-right and up-down shift to fit my values. There were other formulas, but I've chosen this one to follow up on until disproving it because it fits my first impression.
More...

I would focus on the histograms instead. The tan curve is certainly interesting (from looking at it you can guess at the shape of the histogram) but it's synthetic, since the x-axis doesn't really represent anything.

Not all histograms are bell-shaped, but they tend to be for bar-to-bar returns (with fat tails).
 
Quote from zedDoubleNaught:

Thanks dave4532 for the link, this is the type of thing to study I was looking for.

darkcanuck -
Here are the histograms, looks like they are trying to approach bellish curves. It's got the histogram of all the data from the 10 non-contiguous (or non-continuous) weeks of 1100 values, and the second one is the histogram of the average set with 110 values. The average is not so smooth, presumably because it only has 100 values.

I'm not surprised, I've found most histograms come out looking bellish. "Bellish" because I've seen on other threads that a data set of 100 or 1100 is probably not enough to be meaningful, and people disagree about what kind of bell it is. I'll stick with "bellish" as simply meaning: there's more in the middle than at the ends.

attachment.php


For the original swooping curve, I got this formula from eureqa:

0.001402044*tan(0.023389222*index - 1.3131371)

My guess is this means it is a tangent, stretched out to extend across my 110 values, and a couple of numbers to adjust the left-right and up-down shift to fit my values. There were other formulas, but I've chosen this one to follow up on until disproving it because it fits my first impression.

(the attachment is the same jpg as the posted screenshot)
More...

Nazz's post pretty much explains it all. The anamolous behaviour at the tails have been a thorn in the side of financial practitioners for a very long time. Many financial models disregard the existence of these things, and work just fine until a tail event; then...Kaput!

Your intellectual curiosity will take you far.
 
Thanks nazzdaq, darkcanuck and circadian for the input.

After thinking about it a bit, I agree with darkcanuck: the curve is the histogram curve unfolded with the x and y axes reversed, and the x axis replaced with an index of all values instead of a count. So the large ones, very few, don't expand the x-axis much, and they look steep; the middle values, there are a lot more and close together, so the expand the curve and since they're close the slope looks almost flat. Trying to figure out where the next value will fall on the line is like trying to figure out which x-axis value on the histogram will increase by one.

So, I'm putting this one in the "interesting-but-not-very-useful" category.
 
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