Digital ACSTrend - page 28

[JohnLast]

Maximum Lyapunov exponent

Let see what I did.

I took the 5m chart from friday from 0:00 to 17:00 PM from the History:

After that I detrended the close: S= ln ( P t/P (t-1) ) with Excel

S- logarithmic return of time t

P- Price at time t

After that I copied this to a dat file.

After That I started the program with the defaults.

Well it is true that the program starts, but it looks like it does not stop. When it is ready with the calculation the program set the output. Anyway the program did not stopped working after the output is ready in its directory.

So I have a maximum Lyapunov exponent of: 0.9716

The predictability horizon is 1.0/L or 1/0.9716:

1.29 of 5 minute bars.

So definitely on Friday it was possible to predict the New York session.

Anyway the program did not stopped after the output is ready (That creates the illusion that the output is not ready and that it takes too much time) after a while the maximum exponent started to appear negative and very low positive. That means we had a possibility for a deterministic chaos. Is that possible?

Anyway my system performed great friday. Unfortunately as I am not a day trader but a hobbyst and I was not able to profit.

The software is here

Lag Space

This software is innovative because he uses a Neural Net to calculate the optimal embedding dimension. Really great it is accurate and authomatic.

Why we are doing all this? What is the point?

The idea is to measure the predictability horizon. Imagine that there are some attractors in a multidimensionnal phase space. Those attractors attract the price movement following some very complex orbits. The orbits can be clear or unclear, they change all the time. It is a complete mystery.

The maximum lyapunov exponent is a measure of the current state of the system. It answers the question are we in a predictable market state or not, and how large is our predictability horizon. I believe that a state can stay for a while and we can profit while it is still there. Anyway the monitoring of the Hurst exponent and the entropy will show us any sudden change in the system.

The idea is as follows: You measure the predictability horizon for a day at the New York open. So you measure the Asian and the European. And you train your neural nets on that data if you have a sufficient predictability horizon.

This is just theory and hypothesis. Do not forget that. But I feel with that We are really deep into the unknown and unexpored area of the technical analysis. Except several scientific articles there is nothing. Look at the attached article. What we do is to apply this to day trading. And we do not use the false nearest neighbour but a neural net for the embedding dimension.

[Jeanyves Torres]

Lypunov_Correlation_dimension indicator

Well We worked hard this week-end ! lol

Another indicator in the spirit of this thread

the Lypunov_Correlation_dimension

I found the code, but I do not know which settings to put inside

Regards

[e-mail]

[JohnLast]

Lyapunov exponent for mt4 not yet

It looks like it is wrong.

It looks like we did a different indicator, that looks like inversely correlated with the price.

[Jeanyves Torres]

HI john

Well, I do not know how to program "derivatives"

I am going to write a true Largest Lyanpunov Exponent from the source code

Rgds

jaguar1637

[biddick]

[JohnLast]

New indicator

In fact when I inverted the lyapunov indicator and added jurik smoothing I obtained the same indicator as the entropy indicator ?! Of course the indicator is not checked.

What is strange is that Pava did not find any patterns?!

[pavaka]

...

John Last:
In fact when I inverted the lyapunov indicator and added jurik smoothing I obtained the same indicator as the entropy indicator ?! Of course the indicator is not checked. What is strange is that Pava did not find any patterns?!

I was referring to the illustration you presented before...no useful patterns...I'll stick to my guns & roses this time...unless you show me one...

[JohnLast]

Patterns

I was just joking LOL. Anyway everybody is welcome for pattern identification.

Even if this is not the Lyapunov exponent, however we can keep the name because he deserves a name for an indicator.

This time I used instead of SMA a JJMA. Of course you need the JJMA indicator and its libraries at the first pages of the thread.

https://www.mql5.com/en/forum/180729

Basically the heart is:

MathLog (MathAbs(iCustom(Symbol(),Period(),"JJMA",JMA_Period,JMA_Phase,0,0,0,ii)/iCustom(Symbol(),Period(),"JJMA",JMA_Period,JMA_Phase,0,0,0,ii+1)))

Lg (Absolute value(JMA ii/JMA ii+trajectory))

Anyway this looks interesting.

[JohnLast]

Space trajectories

On the previous posts I showed a picture of the Space trajectory of the EUR/USD. How can this be interpreted?

Initially the dream for quant scientists was:

Rather than look at the time series unfold over time, they are looking for a type of order that underlies the trajectories of the system state dynamics as it unfolds over time. The plot of the trajectory may show structural order that may appear random in the time domain. One of the most popular attractor signatures is the well known Lorenz attractor, which is better known to popular literature as the butterfly effect.

Something like the Lorenz attractor in theory it would be nice. But it does not exist.

Anyway on the plot we do not have a stable trajectory. However on the other hand I attach a plot of the Space trajectory of the random walk. Anyway do you see the difference. In the EUR/USD the trajectories are centered with some interesting outliers and on the random walk they are dispersed.

Anyway we do not have a clearly defined attractor.

"One of the fundamental truths about the markets is that the dynamics are nonstationary," Norman explains. "We see no evidence for the existence of an attractor with stable statistical properties. This is what characterizes chaos -- having an attractor with stable statistical properties-- so what we are seeing is not chaos. It is something else. Call it an 'even-stranger-than-strange attractor,' which may not really be an attractor at all.

Intelligent Trading

[michaelB]

JohnLast

It appears I've lost track of all the indicators.

In post 264 and 273 there are charts with aqua and magenta dots on top of the price bars. Can you please repeat the name of this indicator.

Thank you for all your help.