Fractal Analysis?

dtrader98 wrote:

"Also, signal definition of a cycle is pk to pk, or trough to trough (like one sine wave).
But looking back at your definition (pk to trough), that is about a half cycle in basic signal terminology. Although, as you mentioned the data and predictions are aperiodic, the standard zero crossing or pk to pk terminology should still apply IMO."

Yup, you are right. A cycle is peak to peak, or trough to trough. I wrote the original last night when I should have been asleep.

In the picture, 8/03 to 8/07 is one cycle, 8/07 to 8/10 is another. There's some carryover as the picture was taken in the middle of an aperiodic cycle.

dtrader09 wrote:

"Here's how I'm interpreting it (graphic attached). If only the yellow line is prediction vs. actual, that's only 3 days (8/3 to 8/6?). "

Note quite. I guess I'm not very articulate when it comes to writing posts. But the part where you outline as 'Predict' is spot on.

What I meant to get across is that the overlay as you marked it where the cyan line is imposed on the prices is the window it uses in its calculation. And in the overlay you've outline, there's a little yellow segment in continuous cyan line that signals that the window is over with the close of that last bar and the continuous cyan line is the projection going forward.

All vertical bars marks highs and lows of the projection, with the vertical bars to the left marking the high and lows of the previous projections, left there to show how it has done so far on the actual prices. That's to show its performance.

dtrader98 wrote:

"Whereby, actual data is green bars and prediction is light blue (cyan) line. Am I interpreting that as you intend?"

Yes. I guess I was articulate enough to get this point across. Hurray for me!!
 
Just like any term "fractal" has and will progress in its definition as time progresses.

We have progressed from:

A geometrical or physical structure having an irregular or fragmented shape at all scales of measurement between a greatest and smallest scale such that certain mathematical or physical properties of the structure, as the perimeter of a curve or the flow rate in a porous medium, behave as if the dimensions of the structure (fractal dimensions) are greater than the spatial dimensions.

to recently:

A fractal is a rough or fragmented geometric shape that can be subdivided in parts, each of which is (at least approximately) a smaller copy of the whole. Fractals are generally self-similar (bits look like the whole) and independent of scale (they look similar, no matter how close you zoom in).

I personalize the definition for the trading environment to show that:

Fractal charts are specific and exact chart environments that can be subdivided in equal and progressive parts. Progressing from largest to smallest, each is an exact sub-set of a larger chart increment. Fractals charts are absolute bits of the whole but independent in the oscillations each create on each greater or lessor increment. They create identical oscillation types and extremes, no matter how close you zoom in.

An easy way to visualize this is to think of the ocean. In between high tide and low tide they are an ever varying number of waves. If one could determine where high tide and low tide were not only established but more precisely confirmed, then one would know the direction the waves were coming from with an extremely high degree of probability. This gives us the short term direction of the tide. The exact same model can be applied to price movement and the short term direction is then relative to the chart increment that is created to view that price movement.

Math can sometimes be confusing and for the most part trading is not a great place to apply it but I find fractals easier to digest.
 
One thing about fractal analysis is that you need enough data for it to have any meaning. More precisely, you need enough cycles for the data to have any meaning. If the cycle for a data set is four years, as determined by R/S analysis and the largest Lyapunov exponent, then you need to have historical data back far enough to cover enough cycles. I believe 10 is the recommended minimum number of cycles.

If you only use 2 years worth of historical data, when in reality you need 40 years, your results will be meaningless.
 
Quote from panzerman:

One thing about fractal analysis is that you need enough data for it to have any meaning. More precisely, you need enough cycles for the data to have any meaning. If the cycle for a data set is four years, as determined by R/S analysis and the largest Lyapunov exponent, then you need to have historical data back far enough to cover enough cycles. I believe 10 is the recommended minimum number of cycles.

If you only use 2 years worth of historical data, when in reality you need 40 years, your results will be meaningless.
More...

I absolutely agree with having enough data but if you substitute Constant Volume Bars for daily bars you can create some really interesting charts with only 90 to 150 days of data.
 
"Could you be a little more informative than "he's good"? Does he make you regular money or provide you with just interesting reading?
Does he trade indexes? futures? stocks? The site was somewhat threadbare in specifics, especially the results page."

Answer to the first part is both. Yes I've made money and yes it's interesting reading. Short and to the point. No more than couple minutes a day, but again if u follow his advice I think u lose money if you can't spend all day in front of a screen. His primary focus of his service are the s&p's..but he also has a little focus on gold and sometimes silver and oil - depends on the day. This is what I like about him. It's a very short, concise look at the s&p's...so u keep it simple. Sure enough soon as I start hyping the guy he'll probably crap out. But in the almost year I've been reading him daily, I have found his service very useful.
 
Quote from Kuran47:

dtrader98 wrote:

"Also, signal definition of a cycle is pk to pk, or trough to trough (like one sine wave).
But looking back at your definition (pk to trough), that is about a half cycle in basic signal terminology. Although, as you mentioned the data and predictions are aperiodic, the standard zero crossing or pk to pk terminology should still apply IMO."

Yup, you are right. A cycle is peak to peak, or trough to trough. I wrote the original last night when I should have been asleep.

In the picture, 8/03 to 8/07 is one cycle, 8/07 to 8/10 is another. There's some carryover as the picture was taken in the middle of an aperiodic cycle.

dtrader09 wrote:

"Here's how I'm interpreting it (graphic attached). If only the yellow line is prediction vs. actual, that's only 3 days (8/3 to 8/6?). "

Note quite. I guess I'm not very articulate when it comes to writing posts. But the part where you outline as 'Predict' is spot on.

What I meant to get across is that the overlay as you marked it where the cyan line is imposed on the prices is the window it uses in its calculation. And in the overlay you've outline, there's a little yellow segment in continuous cyan line that signals that the window is over with the close of that last bar and the continuous cyan line is the projection going forward.

All vertical bars marks highs and lows of the projection, with the vertical bars to the left marking the high and lows of the previous projections, left there to show how it has done so far on the actual prices. That's to show its performance.

dtrader98 wrote:

"Whereby, actual data is green bars and prediction is light blue (cyan) line. Am I interpreting that as you intend?"

Yes. I guess I was articulate enough to get this point across. Hurray for me!!
More...

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Hey kuran,
going back to your comment on chaos theory. Have you ever tried to apply Lorentz mapping to stock data? Or tried constructing phase state space diagrams of the markets?

Or how about using AI? If you get a chance, read the predictors, there's some good layman's descriptions of the paths and pitfalls to using AI.
 
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