How can I tell the difference between a FOREX chart and a PRNG? - page 30
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The author of this thread posed an outwardly very simple (in formulation) but profound question: how to distinguish between a real quotidian and a HSPC?
The local academics were quickly led away and started demonstrating their knowledge of some minor details, up to and including inventing another bicycle and putting it into a kodobase.
What difference does it make which formula is used to calculate the ACF? Much more important is the program for calculating the ACF, which is what most economists use to analyse economic data. No. Some indicator from a DSP specialist, Matcadas with Matlab. Are these all specialised packages for analysing economic data? No. Consequently, the circle of economists that use these packages is very small. Why are results of calculation of ACF in specialized packages, which have millions of users and have caught all the bugs long ago, not given? Who established algorithms and their correct application?
We could have skipped mentioning special packages. But this thread is open for discussion of a general task, and ACF is only one step in solution of this general task. If we had discussed it in the framework of special packages (EViews, R ....), we would have understood at once that ACF is a trifle, the first steps of analysis which potentially could answer the posed question are made by other calculations. Besides, after calculating the ACF, we would need to take a few more steps to answer the question of the topic.
And, most importantly, we would be stepping on the methodology of statistics, which always casts doubt on any figure obtained. As for ACF, correlation values in ACF must necessarily be accompanied by a probability that will indicate the level of confidence in the resulting correlation values. Experience in using ACF in this form shows that very often this probability revolves around 0.5, i.e. it is not clear whether it is possible or impossible to trust the correlation value available at this camp.
I propose to return to the first post of the topic. Describe at least in words a list of actions that would answer the question of the topic. And the topic deserves it.
There is no rigorous proof.
The periodicity of volatility changes - a guess can be made. But the series must be long enough and the TF less than 4H. On a sample of 500 observations, as in the charts, it is not certain that a real price series will give such an effect. And it is not the fact that gpsh will not give one realization with the same effect. Or rather, it is a fact that it will have the same effect or more.
The notorious thick tails are actually the presence of "outliers". The series must also be long enough. On a relatively short sample, you can pick a tool that won't give such an obvious effect. An ordinary gpsh, of course, will not show such an effect.
Autocorrelation - there is both. This is nonsense.
Either what has been suggested is to find a criterion of difference for specific TS.
1. This is exactly wrong. The autocorrelation function has really only one definition:
2. But you can think of at least forty-two ways of evaluating it (not calculating it), i.e. of calculating the sample ACF.
2. You are right on point 2, as I told above to Privalov, but the author of this branch of forum obviously has problems with eyesight.
1. On item (1) you are mistaken, and moreover you are mistaken monstrously.
First they invented ACF, then they picked up a formula for it, and then they came up with a modern statistical "definition".
There is no "definition" of autocorrelation. What you point out above is just a convoluted snippet of Kolmogorovianism.
Karl's friend Yule described autocorrelation WORLDWIDE in 1926 - as the correlation-similarity of PUSHES of a single time series or a single sine wave (above I just repeated in WORDS this natural concept for mathematicians of the time). Yule doesn't even have any formula for "serial correlation" as he called it in that article. He only gave graphs of the ACF. The method proved useful, and later Walker formalized it a bit, and the well-known modern formulae appeared only after Kolmogorov's work, circa 1942, by Anderson.
Here is the original page where serial correlation is mentioned for the first time in the world:
There is no single "formula" for autocorrelation, just as there is not and cannot be a single "formula for pattern recognition". All these modern formulas are simply implementations of different private ways of recognising the similarity of a function to itself.
Serial correlation, as its author Yule called it, or autocorrelation, is - in simple WORDS - just a measure of self-similarity of a function. And how to calculate this measure - it is yes, you are right - even one hundred and forty-two ways. The main thing is to have a result.
1942:
That was the end of it.
That's settled, then.
Eh, if only it were that easy!
He'll be digging up Karl and his friend Jürl soon and bringing them here to prove his point....
Eh, if only it were that easy!
Exactly the opposite: it turns out (and so it is) that everything we have in the books is either extremely general formulations or narrow special cases, which, if at all, fit to the fora with great reservations and limitations. Especially taking into account that besides linear correlation analysis (the latter can hardly include nonparametric analysis) there is also non-linear analysis, for example the dynamic time warping algorithm that has already been mentioned on this forum. And this is just the tip of the iceberg.
Opening.
Naturally, all mat statistics methods have limitations on the characteristics of the input data used. And it is clear that the price series of financial markets, due to the presence of feedback, cannot directly be used in these methods without their transformation.
DTW? Maybe a non-linear distortion over time will give something in the search for patterns. But so far it's all theory.
The issue is resolved here: https://forum.mql4.com/ru/54199/page38
faa1947:
.....The text of your code does not answer this question.......
It does. It has the word 'period' in there. But a trader is not interested in a pure "period". As Mark Twain said"history does not repeat itself, it RIFMS".
George Marsaglia mixed tracks of rap "music" and presented them as a perfect random series. He called rap "black noise" which passes all the PRNG tests.
https://tams.informatik.uni-hamburg.de/paper/2001/SA_Witt_Hartmann/cdrom/Internetseiten/stat.fsu.edu/diehard.html
or
http://www.robertnz.net/true_rng.html
So how can it be "random noise" - if we can interpolate them on the player and hear a more or less meaningful periodic polyharmonic signal? It's all about insufficient sampling and quantisation, and not knowing the internal structure of 'black noise'. The DIEHARD test, which can extract periodicity from anything, cannot extract periodicity from rap music because it believes there is no internal signal structure. But it is there. It is the same with Forex - all trading systems (except for our system) can not extract the internal structure of the signal.
Because it is very short.
Radio technicians would never dream of what they call "ToR" - technical assignments. No radio technician would even undertake such a task - to determine parameters of an undersampled signal FOR HIS ONE PERIOD.
Let's generalise a bit, using the concepts of the "What is an INDICATOR?" thread
https://www.mql5.com/ru/forum/137416
1. In fact, for trading purposes, all that matters is WHERE - up or down - the price will go on average. The trader agrees in advance to freeze some of his funds with his broker ("margin") so that his trading position can sit out random price fluctuations - as long as that trader KNOWS exactly where that price will go on average in the direction of his trading position.
There is nothing new in this description, it is just that all novice traders do not accurately understand this, understand what they are doing.
2. So, based on the LEGAL basis of a trading contract, and also on the economic goals of trading - it is important for the trader to know nothing else but TWO positions of the price direction - up or down. Based on this, a good or "ideal" indicator for trading should show only two signals (like a semaphore) up or down. Red or green. All other graphic arts on the screen are meaningless for the purpose of trading. The more so because the human eye likes to play with illusions and visions. An indicator for trading should be an alternation of a red bar and a green one - up or down. And such a bar shows some "good average" value of the price series.
3. Price averages are currently calculated using moving averages (MAs), which are used in the technique. And it is well known that this approach does not work in forex, the most volatile market, with the most unpredictable price movements. So the arithmetic average is NOT a good indicator of the average forex market position. This is where other averages are needed. These other averages can't be simple, because the Forex market itself is complex.
4. The "other" averages in such a complex case must be calculated using complicated methods - statistical ones. And those that are not based on confidence in the RMS character of the random deviations from this very "good average".