From theory to practice - page 463
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We need a measure of "memory" - a specific numerical value of the dependence of price increments on each other in the time sliding window.
This makes it possible to state whether the sum of the increments in that window forms a number belonging to the Gaussian distribution or not.
In fact, the ACF is the Grail, folks! It shows whether we are in a trend or flat area...
You just have to learn how to calculate it correctly, which is what I'm doing now...
It doesn't show, and the definition of a flat is not as difficult as it seems, a flat will happen after the price has passed within the day more than usual, it will be sideways, those who "participate in the conspiracy theory" will say later that the price was reeling in volumes on this day ... in general, it doesn't matter, it's the way the market works - the price passed more than the average for the day (summing the ZZ shoulders within the day, this amount is often repeated), then the news or some other event and there will be a big price movement
calculate ACF correctly, here
https://www.mql5.com/ru/forum/117837/page2#comment_3137982
here https://www.mql5.com/ru/code/9930
And it is not the calculation, it is the analysis, let it be the ACF, i.e. you need to decide what happens next - when and where?
it won't show, and the definition of a flat is not as complicated as it seems, a flat will be after the price has passed more than usual within the day, it will be a sideways move, those who "participate in conspiracy theory" will then say that it was the price that was winding up the volumes on that day... in general, it doesn't matter, it's the way the market works - the price passed more than the average for the day (summing the ZZ shoulders within the day, this amount is often repeated), then the news or some other event and there will be a big price movement
calculate ACF correctly, here
https://www.mql5.com/ru/forum/117837/page2#comment_3137982
here https://www.mql5.com/ru/code/9930
And it is not the calculation, but the analysis, let it be the ACF, i.e. one has to decide what will happen next - when and where?
In my TS, when the price leaves the channel of confidence probability and ACF value < 0 at that moment in time, there will be the most unambiguous "return to the average".
Not really. The ACF in this case is simply the classical convolution of any signal on some limited segment with its copy.
There is nothing unusual about this, nor is there any reason to panic.
How many variables the ACF depends on is irrelevant.
You are right about the terminology. QF is the correlation of two processes and ACF is its special case when they are the same process (stationarity has nothing to do with it).
The problem is this: given a single realisation of a process (our price series), the sampling approximation for ACF will only make sense if the process is stationary. In this case the ACF will of course be a function of one variable.
Everything adds up to something, no matter what you count.
Not always. Generate a large sample with a Cauchy distribution and calculate its mean. What will it converge to as the sample size increases?
Answer: nothing, because for the Cauchy distribution there is no expectation.
mentioned in the topic the need for an autocorrelation function over more than one parameter, this is already a field study, I doubt that a discrete function on a time scale (price series) makes sense to consider over the field
For random processes the ACF is a function of two variables. It only depends on one variable for broadly stationary processes.
Not always. Generate a large sample with a Cauchy distribution and calculate its mean. To what will it converge as the sample size increases?
Answer: nothing, because for the Cauchy distribution there is no expectation.
I was talking about the theory of numbers, not about a particular distribution, there are many regularities in the theory of numbers, but they all appear with a large number of analyzed data, I am aware that there are non-convergent series and so on
well and thinking, there are mathematical methods that allow you to go from a non-stationary series to stationary sequences, now do not want to google, but I read about training neural networks, which teach NS probabilities, but not P(A)=1 or P(A)=0, but the more "smooth patterns" - training cotangent, and getting values from the output of the NS cotangent pass to the calculated value of the probability
here in the forum there is an article called BOX-COX REFORMATION, if you Google it you may find other methods of transformation, not the essence - but to apply to market data any mathematical device directly and hope to obtain a pattern, imho, is a road to nowhere - there is neither periodicity nor stationarity in price series, while the entire mathematical analysis is based on these "two whales"
Well, the variant of research with the help of any mathematical tool is that only statistically repeated regularities can be studied, but alas, they are not very numerous in the markets.
For random processes ACF is a function of two variables. It depends on one variable only for stationary processes in the broad sense.
What is the second variable in your ACF?
In my TS, when the price leaves the channel of confidence probability and ACF value <=0 at that moment in time, there will be the most unambiguous "return to the average".
OK, return to average is what? The average price?
OK, a return to the average is what? The average price?
The expectation of both the increments and the sum of the increments is strictly =0. I don't work with pure prices, mash-ups and such nonsense. Only with increments.
But, I don't impose my TS - alas, so far profit for 5 months of trading =+5%... Sad...
That's why I'm like a wounded lion clinging to ACF.
what would be the second variable in your ACF?
Time, like the first. It seems to say it all here.
The expectation of both the increments and the sum of the increments is strictly =0. I don't work with pure prices, mash-ups, etc. nonsense. Only with increments.
But, I don't impose my TS - alas, so far profit for 5 months of trading =+5%... Sad...
That's why I'm like a wounded lion clinging to ACF.
Once again, the last one.
1. KF-AKF is a function, not a number.
2. KF-AKF says absolutely nothing about the current and future points in time, but only about the average over the sample.
3. Application of KF-AKF to small samples is utter nonsense. I.e., nothing at all.
I am not participating in this discussion any more).
We need a measure of "memory" - a specific numerical value of the dependence of price increments on each other in the time sliding window.
This makes it possible to state whether the sum of the increments in that window forms a number belonging to the Gaussian distribution or not.
In fact, the ACF is the Grail, folks! It shows whether we are in a trend or flat area...
We just need to learn how to calculate it correctly - that's what I'm doing now...
If I wanted to trade with a flat trader, I would try to guess, what would be the difference between them, because even if I succeed in dividing them, the trend TS would be killing the flat TS and vice versa.