a completely random process and FOREX. - page 4

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lna01:
D.Will wrote (a):

The graph is a fully deterministic series, just statistically indistinguishable from a random series. So it is just a good example of a chaotic series :) .

What are you?

don't confuse us please.

A random process by definition is a sequence of random variables. When defining a random process we always talk about variance and variance-matrix and everything else.



And a deterministic process is a process that at any given time you can clearly say what the next state the system will move to.


For standard pseudo-random number generators you only need to know the number at which it starts to predict the series unambiguously. So the series in your picture is theoretically fully predictable.

1. Do you know this number?
2. with an accuracy of 16 digits it cannot generate a sequence of more than (65536) elements.
 
lna01 писал (а): For standard pseudo-random number generators, you only need to know the number from which the series started to be predicted unambiguously. So the series in your picture is theoretically completely predictable.


Candid, it's not that simple. I thought so too, until komposter and I checked MathRand() function. Here's a branch: 'Beginner's question: two curves in different windows'.

Code:

#property show_inputs
 
/*extern int init_start    = 0;
extern int init_end      = 100000;*/
 
extern int iterations    = 1000000000;
 
int start()
{
    int tmp, pre_tmp, count_23281 = 0, count_16827 = 0, count_23281_16827 = 0; string res;
    //for ( int start = init_start; start < init_end; start ++ )
    {
        int start = 1;
        MathSrand( start );
        for ( int i = 0; i < iterations; i ++ )
        {
            pre_tmp = tmp;
            tmp = MathRand();
            if ( pre_tmp == 19169 ) //23281 )
            {
                count_23281 ++;
                if ( tmp == 15724 ) //16827 )
                {
                    count_23281_16827 ++;
                    res = StringConcatenate( res, count_23281_16827, ": Init value = ", 
                          start, ", interation # ", i, "\n" );
                }
            }
            if ( pre_tmp == 16827 ) count_16827 ++;
        }
    }
    Comment( "Чисел 23281 - ", count_23281, "\nЧисел 16827 - ", count_16827, 
                "\nЧередований 23281 с 16827 - ", count_23281_16827, ":\n", res );
    return(0);
}
P.S. I guess you're right. But the period of this sequence is obviously very large. The grain defines the whole sequence, but the segments of it starting from the same number are different.
 
D.Will писал (а):
Moreover, there are systems whose operation is fully described *e.g.
y(n+1)=a*y(n)*(1-y(n);
which is almost impossible to predict. at a->4.

Such processes are called deterministic chaos.

Exactly that practically, in reality we will simply never know the value of a parameter with sufficient accuracy. Nevertheless, chaotic processes are much more predictable than random ones. But we cannot distinguish between them statistically. It follows that statistical arguments are irrelevant to the question of market predictability.
 
I have decided to reduce the determinism of the pseudo-random number generator by shuffling the series of random numbers several times.

close all;

N=1000;
r=NORMRND(0,0.0077,1,N);

r1=r;
% shuffle
for i=1:1:10000
i1 = fix(rand*N)+1;
i2 = fix(rand*N)+1;
c=r(i1);
r(i1)=r(i2);
r(i2)=c;
end;

figure;
%r=r-0.5;
for i=2:1:length(r)
r(i)=r(i)+r(i-1);
r1(i)=r1(i)+r1(i-1);
end

grid on;

plot(r);
figure;
plot(r1);

result


mixed


There. got rid of the periods. so what's the use?
 
lna01:
D.Will wrote (a):

Moreover, there are systems whose operation is fully described *for example

y(n+1)=a*y(n)*(1-y(n);

which is almost impossible to predict. at a->4.



Such processes are called deterministic chaos.




Exactly that practically, in reality we will simply never know the value of a parameter with sufficient accuracy. Nevertheless, chaotic processes are much more predictable than random ones. But we cannot distinguish between them statistically. It follows that statistical arguments are irrelevant to the question of market predictability.

with sufficient precision. which is it?
All theories concerning d.h. analyse either the equations of models or history (extracting statistical regularities).
And what do you mean by statistical characteristics? mo and std? and who says it's a measure of the equivalence of two sequences?
 
Mathemat:
lna01 wrote (a): For standard pseudo-random number generators, you only need to know the number at which the series started to be predicted unambiguously. So the series in your picture is theoretically fully predictable.

No, Candid. I thought so too until komposter and I checked MathRand() function. Here's a branch: https://forum.mql4.com/ru/6187 .
I think the effect of repeating pairs could be, for example, if the lowest 16 digits of 32 are taken as a random number. But if not them, it might not exist :). This does not invalidate the fact of predictability. The situation will become more complicated if with the same start number you get different sequences. Then we will have to think only about partial predictability :).
 
D.Will писал (а):

The trick is, with enough precision, which one is it?
The question can only have an answer for a specific problem.

P.S. The "probability density" is also a statistical characteristic. Nor does it guarantee reproducibility of all process characteristics with the RNG.
 
lna01:
D.Will wrote (a):



The trick is, with enough precision, which one is it?


The question can only have an answer for a specific problem.



P.S. The "probability density" is also a statistical characteristic. And neither does it guarantee the reproduction of all the characteristics of the process with the RNG.

Even for a particular problem you cannot theoretically justify it since changing a process parameter by 10^-100 may change its dynamics beyond recognition. (bifurcations and so on)
so computers are not really appropriate for analyzing such processes. (from a fundamental point of view). Only their probabilistic and descriptive modelling is possible.


lna01> P.S. The "probability density" is also a statistical characteristic. Nor does it guarantee the reproduction of all the characteristics of a process by a RNG.


how do you imagine it??? how to reconstruct something by the distribution law of a random variable??? such a task cannot exist at all.
If I cited a histogram it was only to show that the distribution of a random variable is the same as that of eurusd 1D.
 
D.Will писал (а):
lna01:
D.Will wrote (a):

The trick is, with enough precision, which one is it?


The question can only have an answer for a specific task.

Even for a given problem you theoretically can't predict it. Changing this parameter by 10^-100 may change the dynamics of the process beyond recognition. (bifurcations and so on)
so computers are not really appropriate for analyzing such processes. (from a fundamental point of view). Only their probabilistic and descriptive modelling is possible.
Well, if for example for some ranges of parameter values attractors can be identified, that would imply partial predictability. In that case, the limits of those ranges will determine the "adequacy" of the parameter definitions. About insufficiency of computers for analysis of such processes I completely agree with you - the main thing in this business is the head :)
If I cited a histogram it was only to show that the distribution of a random variable is the same as eurusd 1D.
Right. And I asked: "So what?" :) I repeat: the series that you pose as random is not random. It's just that for tasks for which only statistical characteristics matter, it can be used as random. That is, it would be more correct to write in the title of the topic "RNG Matlab and FOREX" :) . Actually, the main idea of my posts is that there is no reason to consider Matlab's RPM as "absolutely random process".
 
lna01:
D.Will wrote (a):

lna01:

D.Will wrote (a):



The trick is, with enough precision, which one is it?





The question can only have an answer for a specific task.



even for a specific problem, you can't theorise about it. as changing this parameter by 10^-100 can change the dynamics of the process beyond recognition. (bifurcations and so on).

that's why computers are not quite appropriate for analyzing such processes. (from a fundamental point of view). Only their probabilistic and descriptive modelling is possible.

Well, if for example for some ranges of parameter values attractors can be identified, that would imply partial predictability. In that case, the limits of those ranges will determine the "adequacy" of the parameter definitions. About insufficiency of computers for analysis of such processes I completely agree with you - the main thing in this business is the head :)

If I did give a histogram, it's only to show that the distribution of a random variable is the same as eurusd 1D.


Right. And I asked: "So what?" :) I repeat: the series, which you position as random, is not random. It's just that for tasks for which only statistical characteristics matter, it can be used as a random one. That is, it would be more correct to write in the title of the topic "RNG Matlab and FOREX" :) . Actually, the main idea of my posts is that there is no reason to consider Matlab's RPM as "absolutely random process".
Well, there is nothing abnormally random. the topic is so named because it emphasises the similarity between "abnormally random" and "non-random".

If you look above, I gave an example where the entire sequence is mixed several times. and displayed both one and the other sequence.
This is an attempt to downgrade the determinism of the GSF. the character of the movements is the same.
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