Random Flow Theory and FOREX - page 33
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OK, let me ask it another way. Here's a fractal tree - where's the noise in it?
P.S. Nice tree. Tell me, what is the difference, you do not see very small branches because of insufficient resolution of the picture or because they are not "counted out"?
Peters describes well the concept of noise in fractal processes: local randomness, but global determinacy.
In my humble understanding, fractal has no noise in principle, just by definition of fractal, at least in view of its integrity as an object. Its nature is such, while noise of course can be found everywhere, even where it does not exist. DSP supposes presence of noise and effective methods of fighting it. But it is more of a philosophy, of course.
But Peters, damn it, ....
OK, let me ask it another way. Here's a fractal tree - where's the noise in it?
P.S. Nice tree. Tell me, what is the difference, you do not see very small branches because of insufficient resolution of the picture or because they are not "counted out"?
P.S. When I wrote this, I did not see your answer yet
I finally have some free time. I will try to present a coherent account of what many people have come up with in trying to answer the questions posed. And I will try to present it more holistically + my point of view on all this. At the same time I shall try to explain in simple language, without resorting to special terms, where it is possible. And I shall tell all things known to you, but under a little other angle, as I see it.
So let's begin.
The first thing I would like to find out is if the price is continuous or discrete. If we go from the definition that the price is a product of supply and demand, it turns out that if there is no supply and demand, there is no price either. And if there is demand, and there is no supply, the price does not exist either until there is a supply (and vice versa). The question arises as to how it (the price) can be measured in this case. The reasoning on this subject leads to a magnificent phrase of Mathemat: "There is no peace, until I measure it". I will modify this phrase a little, "there is no price until I measure it". It seems beautiful all right, but this position leads to the fact that many processing methods lose their physical meaning, the same MA (calculation of average), all extrapolation and interpolation methods too, as there is no price between measurements. But the strange thing is that if I put 2 fingers in a 220V socket (measure voltage :-)), it will be there exactly (well almost always as they say in mathematics), and all my life experience tells me that even if I don't do it (don't measure) the voltage is still there. Extending this knowledge to the price, I stand on the position that the price is always there, i.e.the price is continuous (and it has no gaps, studs). All of these gaps are due to imperfect methods of price measurement.
How do we see the price (how it looks on the screen)?
It begs the analogy of ADC (analog-to-digital converter), there is quantization on the Y-axis and sampling on the X-axis. (If you are not familiar with ADC, I recommend to spend some time studying it). Errors are peculiar to this transformation, in our case it is 0.5 (minimal step of price change) on the Y-axis. But with X-axis (usually time) is more interesting, there are errors, too, and they are associated with the inaccuracy of the generator that sets the sampling rate (and it (the frequency) is tightly linked to delta_t sampling period) Remember, the frequency is measured in Hz = 1 / sec. We are just used to this value = const. They try to do so, it simplifies a lot of calculations and work of various devices. That's why I think it's not correct to say that we have data arrival period (sampling period) but not sampling frequency. We then lose common sense in our reasoning. I would very much like to keep it. So I argue that there is a sampling rate, only it has one property that is not familiar to us - it is not constant.
Why is the sampling rate not constant?
Everything seems to be simple here and you've come to this conclusion yourself. Not all traders in the world can press the button once and for all. Therefore, the arrival period is not constant, but it changes all the time, hence the sampling rate also changes.
So how is the price measured?
In practice it often happens that something must be known (measured, estimated), but the device does not measure the required value (figure). In such situations, resort to expert advice. A group of experts is gathered (in the field of knowledge), bad experts are eliminated according to certain criteria, while others are trying to answer the question. Often there is a situation where there are two experts who give opposite assessments (measurements) and they stick their necks out (considering themselves experts on everything) and you scratch your head. In the market it is the same, but the quantity of experts is much more, and they do an excellent job with nitwits. Let's say, the U.S. Federal Reserve (the 1st expert) has set its price of USD/GBP, and the Bank of England (the 2nd expert) has a price that differs much from the 1st expert (for example, 20 points). All other market participants will attack them like a pack of hungry wolves, and will bite, gnaw and do not even get bit - the main thing is to bite them (and the ping would be faster, to gnaw these fools before they come round), because this is pure Arbitrage, a completely safe strategy (of course under certain conditions (the main thing is not to gnaw until the end)) (wish I were a part of it with a good ping :-)). Thus, the market gives a pretty good estimate of the price.
Why sampling rate is so important.
There is a very simple rule, the higher the rate of change of the process under study, the higher the sampling rate should be and the higher the sampling rate, the better (more accurate the representation of the original continuous process). Just imagine what a sine wave after sampling would look like at 2 counts per period and 100 (at 100 it looks more like the original sine wave). And there is a great theorem by Kotelnikov (read it) https://ru.wikipedia.org/wiki/%D0%A2%D0%B5%D0%BE%D1%80%D0%B5%D0%BC%D0%B0_%D0%9A%D0%BE%D1%82%D0%B5%D0%BB%D1%8C%D0%BD%D0%B8%D0%BA%D0%BE%D0%B2%D0%B0
If we do not follow this theorem, things get very bad. Let me explain by example, we measure the speed of the plane, say 800 m/s, and take the next measurement one hour after the first one. The plane has already landed at the airport, its speed = 0. This is a gap in pure trader terms. On Friday the price is ****, and on Monday **** the gap. We have no measurement in this time frame !!! (Kotelnikov's theorem does not hold). And imagine what a gap would look like if the sampling rate was say 100 MHz, that's 100,000,000 measurements (counts, ticks) per second. I think there would be no gaps. And a nice smooth curve could be plotted.
How to make our measurements better (more accurate, faster, more powerful).
The first very important thing is to increase the sampling rate. The correct brokerage companies (not "bunkers") try to get quotes from several sources for this (it's better to have all of them). And here become very interesting for brokerage companies (and probably for traders as well). The first is how to choose "the right quotes provider". I think in view of the above it is clear, we need those with the maximum number of deals (measurements) per time unit. Secondly, broker will never reveal to us the sources of getting quotes (although I think there is an exception, its description is given below), since a trader will have the opportunity to play against the broker. But from my point of view, there are special brokerage companies (brokers, banks ...) that deserve a close look. Unfortunately, I have never seen an entry quotation flow for brokerage companies and I have no access to it. But I would really like to know who is the first of brokerage companies (banks, brokers ...) to make a deal on Monday (in gaps) and for what currency or precious metal. Because it is logical to assume that either they have good experts, or they create an artificial gap that is closed later, like a decoy. This knowledge can be valuable.
Secondly, it is important to understand that if we work with pips (as they are now), we doomed ourselves to the fact that the processes with period of oscillations less than 2 min are not available for analysis. And based on practical considerations and the time required to recognize an oscillation (frequency estimate, amplitude and phase, even a simple sine) rises to 30 minutes (somewhere earlier in this thread I wrote about it). At a good rate of price change it is 60-80 points.
The third thing is to refuse from the construction of bars and switch to another representation of the price. After all, we have invented so many ways to analyze a random variable along the Y-axis (MA, RSI, etc.), and we forgot about the X-axis, while it is a random variable and it too should be handled correctly and carefully. The first thing is to take the average for 5 ticks and construct it as a point on the plane with confidence intervals of estimations of this random value for each of the axes. It is necessary to think, look and examine many variants, most likely this curve will become smoother, and therefore more predictable. Perhaps, it will give us a needed advantage over other experts and our estimates will become faster, better and more accurate. There is, however, one thing that confuses me - "false tics". Maybe I'm wrong, but for correct calculation of minutes in MT4 it is necessary to generate a false tick at the beginning of each bar if there were no trades at all (it seems to be the simplest solution). If so, it's true (I don't know for sure, developers must answer). It is necessary to remove these ticks somehow, I think it is very important. It follows from measurement theory, it is better not to deal with false measurements and try to avoid them at all (and not to generate them by yourself in any case).
I suggest (and those only), and even many have already I think moved to a different kind of chart representing the price. Simply swap the Volume and time (look at the chart). The time will be compressed in a quiet market and stretched in a fast one. Indicators will lag less. And this is nothing else but change of data frequency (sampling frequency); in the fast market there will be more of them (measurements), we will be able to analyze a fast running process. We will refuse from HLOC bars and build confidence intervals instead of boundary points.
After all, the idea is to bring an unsteady random flow to a stationary one using various transformations. And we will not be far from a good TS there.
With the above transformation we reduce one of the most important properties of a nonstationary flow to a stationary one (see page 1) - it is a moment function of the first order, called intensity of flow (IF) or the number of transactions (measurements) per unit time.
Wish if they tell you some seemingly undisputable things, always question everything. This is the only true way of a researcher. You cannot fly, and we flew. You can't reach the moon and we've already trampled it, you can't make money in the market.... Where does the money go? Or maybe the law of conservation does not work any more: if you lose somewhere, you gain somewhere. You cannot win in the long run, maybe not if you play like in a casino, but if you don't play, but think, analyze, find some patterns and use them. And defeat your opponent time after time, until he starts to change, change - change you too. Become better, faster, more accurate, enrich yourself with knowledge. And then come back to the special case, the brokerage house will open to you everything at its entrance (all the quotes), and will help you in everything, up to the special courier who brings the money to your home and takes care of the flowers for your beloved mother-in-law's birthday. You only have to work with him, on his team of experts and not against him.
lna01
For the doubling (quadrupling of periods), if I understood correctly what it says, very quickly looked diagonally. I had to deal with something similar. We had to make measurements when Kotelnikov's theorem was not fulfilled, there was a very fast process. And there were interesting effects, we almost started to believe in cabbalism, until we found out what was there and how. The process under study would degenerate into a constant, or there would appear some stable oscillations, which couldn't even be close to it. These are resonance effects also known as Lissajous figures. There you can do something (try to bypass Kotelnikov's theorem) and even there is some mathematics about it, but in practice it all falls apart because of the inaccuracy of Fdisk (although the models seem to work). At superhigh frequencies F-disk is not constant (unfortunately this is our case).
P.S. By controlling sampling rate you can get anything you like from constant, say, 0, to the curve, that you see on the screen :-). It's to a question, that a number rules the world, ...... I hope, that no one runs this number (and I'm not going to, my tasks are much more modest). But one should not forget about this number when processing incoming information. I forgot (when I saw the money on the screen :-)), though I used to consider myself a DSP expert. Now I have changed and am not a specialist, but rather a person who has a certain amount of knowledge in this area. Don't step on this rake, you know about it now. I wish I had understood it earlier (to remember, to see the market from this angle), how many years have been lost, I hope it was not in vain after all
That's great!
It takes a while to get to grips with it.
http://grasn.narod.ru/002.djvu
И вот если мы эту теорему не выполняем, то становиться все очень плохо. Поясню на примере, мы измеряем скорость самолета допустим 800м/с, а следующее измерение делаем через час после первого. А самолет уже сел на аэродром, скорость его =0. Это же гэп в чистом виде в терминах трейдеров. В пятницу цена ****, а в понедельник **** гэп. У нас нет измерений в этом промежутке времени !!! (Теорема Котельникова не выполняется). А представьте как бы выглядел гэп, если частота дискретизации была допустим 100 Мгц, это 100 000 000 измерений (отсчетов, тиков) в секунду. Я думаю гэпов бы не было. И можно было бы построить хорошую плавную кривую.
Why isn't it fulfilled? The theorem, the one I cited earlier, states that the sampling rate should be twice as high as the highest frequency component:
Fd>2*fmax.
AOG situation, - VS on the ground. The source signal (measuring speed) shows zero all the time. And why don't we fulfill the theorem? :о)
In our case - no one trades on weekends, and there is an economic process, plus emotions and panics, the gap on Monday. What does the Great Kotelnikov and the CSO have to do with trading? I understand that everyone explains the phenomenon to the extent of his knowledge. Perhaps, one can with interest listen to traders - biologists, zoologists, chemists (they have many laws there or dental technicians. ButTHIS is different, the different nature of THIS!!!! COC - not helpful, along with Kotelnikov!
to Candidlna01
For the doubling (quadrupling of periods), if I understand correctly what it says, ...
That's not what I understood it to be about.
I don't want to repeat the main text of the post, because I have already written, that I don't consider correct the identification of frequency of ticks with a sampling frequency. Generally speaking, since the vast majority of ticks are one-point, the proposed transformation is very close to "let's consider the derivative at any point constant modulo".