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This is a short 6 minute video on Fibonacci numbers and plant growth. It gave me an idea, it will take me a while to explain it.

A long time ago in a century long past I was in ET school. I was anxious to get through the basics and get up to radio communications theory. I always wanted to understand what "AM" and "FM" really meant.

When I finally got into the class they showed how "AM" stood for "amplitude modulation" and how the first transmitters took a radio frequency carrier wave and imposed intelligence on it. In the beginning, (I will use round numbers here) the carrier was a signal cycling at 1,000,000 cycles per second and the intelligence was simply a 1000 cycles per second tone imposed on it. If you looked the carrier without intelligence,(modulation) on it on an oscilloscope you could see a sign wave or a solid blue (or green, depending on the screen) band across the scope. There reason for this is that you can adjust the time scale of the presentation. If you make the time scale very small, you can see the voltage of each radio frequency wave rise and fall, if you make the time scale larger, the wave rise and fall so fast that they run together.

This larger scale is nice because when you impose the 1000 cycles per second tone on to the carrier wave, you can see the voltage of the carrier wave rise and fall at the 1000 cycles per second rate.

Wow! I finally understood "AM". There was only one problem. I asked the instructor, "What is this switch? Why does it have AM, USB and LSB on it? And why do you call this radio a SSB transciever rather than an AM radio?"

You have no idea how long that lecture lasted, I will tell you that by the time was over he had to open a new set of dry erase markers.

I will try to shorten it up. Back when Marconi started with his radios, he saw what he was doing like was shown. A really fast radio transmission wave with a much slower signal changing it in amplitude.

However, some genius, and I do mean genius, looked at what was happening with a spectrum analyzer. Now the best way I can explain the difference between the oscilloscope and the spectrum analyzer is a fish tank. If you look a something from the front of a fish tank, then walk around to the side, you will see the same thing, but it will appear different.

When you look at the AM signal with a spectrum analyzer you realize that the carrier and the intelligence are actually occupying two different frequencies in the radio frequency spectrum. The intelligence will be some amount of power displaced from the carrier at frequency of the intelligence. In other words a carrier of 1,000,000 cycles per second with an intelligence of 1000 cycles per second imposed on it will appear in the radio frequency spectrum as a spike of power at 1,001,000 cycles per second, 1,000,000 cycles per second and 999,000 cycles per second.

What some genius engineer figured out was, we only needed the intelligence in power above the carrier, not the intelligence below the carrier, and we could recreate the carrier at the receiver. So, to save power he suppressed the carrier and the lower side band only transmitted a Single Side Band (SSB) and we typically use the Upper of the two side bands (USB)

I will not go into FM, or frequency modulation and the spectrum analysis of it, it will make your head hurt.

Now, to technical analysis.

We know that chart patterns are fractal, that no matter what time frame you move to, (except maybe in the HFT frame) that the same patterns have some predictive abilities. We also know that they fail. In other words the patterns rhyme but they do not repeat. Much like the flowers and Fibonacci sequences from the video.

Suppose we are looking at the markets from the wrong side. Suppose like the Oscilloscope and the Spectrum analyzer we need to have a different display.

Suppose instead of looking at the charts as price vs. time we turned them somehow and made a spiral chart that would fill in the leaves over time. Then we might have a clearer picture of the cycles.

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I'm going to offer a suggestion which may either simplify or complicate the model you are contemplating.

One of the ways that we can multiplex information (put more than one data streams on a given wave) is by using different different frequency "bands" superimposed on a single carrier wave. To separate them out at the receiving end, one method is to use a series of bandwidth filters.

One of the issues caused by this method is the creation of harmonics - spots where the peaks or troughs of a number of the information bands combine to create substantial distortions of the overall waveform.

I suspect the difficulties in interpreting various derived financial "waveforms" is that they are generally formed by multiple layers of potentially disparate datasets. In addition, sometimes the disruption caused by harmonics is easily misinterpreted because of its gross distortion.

(Just thinking out loud)
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Mean "bandpass filter" not "bandwidth" filter

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Hi Qaz,

Suppose instead of looking at the charts as price vs. time we turned them somehow and made a spiral chart that would fill in the leaves over time. Then we might have a clearer picture of the cycles.

Very well done, Qazulight-san!

You are now ready to proceed to your next level of discovery;


Do not come back until *ALL* the vehicles are washed and waxed!
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Qaz said: Suppose instead of looking at the charts as price vs. time we turned them somehow and made a spiral chart that would fill in the leaves over time. Then we might have a clearer picture of the cycles.

Qaz, your are on a similar path that some of the HFT guys use. To get a bit technical, you can either represent a signal in the "time domain" or the "frequency domain."

When you look at a normal stock chart, you would say it is in the time domain. You can mathematically convert it to the frequency domain. It is particularly useful if you are looking for some kind of period cycle.

To my knowledge, the first book written on this was:

The Profit Magic of Stock Transaction Timing" by J.M. Hurst back in 1970. The cover proudly proclaims: "20,000 hours of computerized data analysis has unlocked. . .

I was able to find my copy and will scan it over in the next few days.

Long story short, a lot of people have spent a lot of time working on detecting consistent cycles in stock prices. Some of this work is done in the time domain and some it in the frequency domain.

Rest assured that a lot of the Math/Physics PHD's that have become financial researchers look in these areas. These folks are looking for any edge that can get. They have the ability to looking at stock prices in the frequency domain in real time. This is the equivalent of your spectrum analyzer for electrical signals. . .

It is vastly large topic with a million different directions to look into. I am sure there are several boards around where folks still debate different aspects of this. I have not kept up to date on the exact approaches being used, and it is not like the top researchers will share their work. They keep the good results close to the vest, trying to generate a little extra return for their hedge funds.

Pretty interesting area you have wondered into . . .

Good luck,

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Back around a gazillion years ago, in a largely analog world, I was working on creating a multidimensional model which could be displayed in a two dimensional world (a color CRT tube). It's easy to imagine a three dimensional image, but by considering adding shape (say distorting a virtual object between planar and a curve at any given point), color gradient at any given point and appearance of texture at any given point, a visual object could display a large number of simultaneous dimensions (hopefully in a way that would be useful).

While pretty cool, and possibly still useful, this is more of a qualitative technique and depends on our personal evaluation. Yoda brings up a good point that both the frequency and time domains are involved and the first step is to strip each individual waveform out from the mess.

While harmonics are easy to calculate, the fun comes in when we consider how the shape (over time) of each wave affects some of the others. That this affect is non-linear in many cases makes the analysis a bit funky. It is the creation of this model which will determine part of the success of a financial institution's use of the data.

Simple or exponential moving average crossovers are simply anecdotal - except so many people use them that their actions become self-fulfilling prophesies in many cases (and when they don't - there is a shrug and the statement "well it was only statistical). The same is true for many other "rules". So these rules add a preference or bias which should be included in the model (what others think matters in this case).

Charts are useful, but don't get carried away with them unless you make the effort to deconstruct them first. On top of that, while the mechanical guys would roll their eyeballs up in the air - macro and politics matters. People change their strategy based on taxes, political climate, unassociated news, etc. and these very real factors have to be considered in real time (and can sometimes trump charts).

(Just some random thoughts)
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"...Suppose like the Oscilloscope and the Spectrum analyzer we need to have a different display..."

Dear Quaz:

The post with links to the Khan Academy was great! Further, I totally agree that another way is needed to view pricing patterns.

I'd like to put my two cents in, if I may. If you want to analyze using statistically self similar ( or 'rhyming') fractal analysis, you'll need to employ the different logarithmic price scaling, other than base 10.

This phenomenon was first noted by a hydraulics engineer, H.E. Hurst, who was studying the very abundant data of Nile River discharge over a very long period of time. In a nutshell, he discovered that the regression to a mean value over time varied according to an exponential factor of 0.5.

Log Price vs. time should not be at all too difficult to plot as most, if not all charts are able to switch to "logarithmic scaling" on the price axis. The problem is that the log scale on the charts which I have access to, as far as I can tell, will only scale to base ten. I wish I knew how to change that on my trading platform.

In order to employ fractal analysis, a scaling dimension is needed. This is not as difficult as it sounds. There's a very simple method called the box counting method. I'm sure that there's software for this. The resulting ratio is nothing more than the change of logarithmic base formula found in any college level algebra textbook. This method gives a good approximation of the 'fractal (Hausdorff) dimension'.

Once you have that dimension, i.e., you'll also have the new logarithmic base! (Which, again, need not be a whole number). Your logarithmic price axis must now be scaled to that base.

I can even think of a few good examples to test it out. One would be to plot dimensionally scaled cumulative money flow into gold over many decades and then 'compare' the similarly scaled price of gold over the same period. Another would be silver and of course, copper. I'll bet that there can be found notable divergences in the scaled price of gold when compared with a properly scaled chart of cumulative money flow just before booms or busts, especially when the cumulative money flow over time is properly scaled.

Ditto for the major indices.

I think that variable logarithmic chart scaling can be accomplished in Excel, but I can't seem to get a hold of a good sized database. I've been looking, though.

As a reference, I'll strongly recommend Paul S. Addison's, Fractals and Chaos. An Illustrated Course. It's a brief overview with examples, and problems which can be solved with pencil, paper, straight edge and compass and a calculator. It's less than 250 pages and available in paperback.

Just a thought. I'm of the opinion that Fractal Analysis is not the holy grail of analysis, but it's 'along the same lines' of looking at price vs. time charts in a different way.

Anyway, I'm way over due for my morning walk along the (still not replaced) boardwalk.

Your shoreline Fool,
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