Random Flow Theory and FOREX - page 13
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I doubt we can talk about speed, let alone acceleration... at least in the same vein as the speed and acceleration of aircraft.
I agree that speed and acceleration are different. But they are both there and there. This approach makes it possible to predict
But then the question of portfolio testing would come up in full force - once again the problem grows immense :-(.
From your article "Speed estimation under foreshortening":
Д(t),V(t),a(t) – детерминированные составляющие соответственно дальности, скорости и ускорения;
DV(t), Da(t) are fluctuation components of velocity and acceleration;
Here is an open press article (attached), it says about our research at the end of the article. And the ACF of real airborne TDS (Doppler frequency trajectories) is given (the Doppler frequency is directly proportional to velocity), see Fig. 9. Compare them visually with the ACF I posted ('Random Flow Theory and FOREX' or here 'Random Flow Theory and FOREX' ). When I saw this curve, I couldn't believe my eyes, I checked it 20 times (I've built it using different methods, now I've checked it via the 3rd method, there is no error).
Alpha, beta and sigma, just laid down in the form of ACF (which are inserted into these equations), is an inertial link of the 2nd order. Physically it performs its oscillations, around a certain level, if no external energy comes, the oscillations are damped. If an impulse comes it (the oscillation) can move to a new level, and it will oscillate again.
If you vary the sampling depth, different oscillations (fast, slow, about what the article says), i.e. the total movement is as if composed of all these oscillations with different (alpha, beta, sigma). Multidimensionality and multidimensionality of motion.
In optimal processing, for every oscillation you need to have a different filter. But this is an infinite number of Kalman filters ;-(. I wrote earlier that further art (trimming calculations) each of us may need different detail of this process to build a TS. And someone, let's say, wants to consider the relationship of different currencies (analogous to the Master-Slave in this article), there is a correlation between them and this too can be put in the model, estimate this movement and direct the energy of forex to your pocket, not all, a little pinch and enough :-).
P.S. I have doubts about the formula (10), something does not fit there. And in the book, too, it seems to be a misprint. I went to Tikhonov because of it, but his ideas are alive and there are his students, Kharisov and Yarlykov, it is difficult just to find them in the Academy, as a last resort I will go to Bogdanov in Tver (author of this article and supervisor of this work and my dissertation at the same time).
For a quotational process (and even its first difference) it is highly questionable, as the process itself is not like a stationary one, much less an ergodic one. Second:
Where do we have normality, Prival?
1. For a quotient process (and even its first difference) it is very doubtful, as the process itself does not resemble stationary, much less ergodic.
2. Where are we on normality, Prival?
1. ACF was constructed for Y-mu, i.e. the "trend" mu=y(x)=a+b*x was previously removed from the quotation process, thus the MOG of the process = const (one of the stationarity conditions 0 in our case). There is no problem for Kalman to determine the "trend" - this is the detrended velocity component. The remainder after removing the "trend" is the fluxation component of the velocity. I agree that the fluctational component is not an ergodic process, but there are areas where it corresponds to the oscillatory link and I think there will be a lot of them on the history (what is called a flat). There are some sections that do not correspond, it means that another model should be used in the filter. There should be many such filters, ideally infinity. When I explained the physics, "like in the receiver, you turn the knob to get a station (trend) and keep it there. Lost a station, turn the knob until it rings aha news, worked off the news, gone again went to spin further. So there you go. But it's more complicated and in formulas."
If a stream of quotes corresponds to the attached model, then everything is OK, we listen to the news, the trend, the flat, etc. When the signal disappears (discrepancy at the filter output exceeds a threshold) all we need is to turn a knob and look for a filter out of the remaining 99 (billion-1) that is more appropriate to the current process (the model embedded in it).
The only thing I want to pay attention to, that nobody cancelled Kotelnikov's theorem, if quotations come in 1 time in a minute (we work by minutes) that processes accessible to us for research have a period of at least 2 min, in practice it is better that frequency of sampling in 5-8 times above maximal frequency. If you project (focus) the work of TS on news, then we should switch to ticks.
2. Probably there is normality, read carefully the condition that says "a straight horizontal flight", it means MOJ=const and does not change, no matter what section of this time interval we take. Find such an area on the quotes and see (+-1 pips within an hour at MOJ=const). Never mind about the interval :-) Superfluous phrase in the article, unrelated to the essence of the research.
And in general my fingers hurt :-) put on headphones.
You need to make a Kolman filter in MQL, here is how it looks like in MathCad
indexes "T", "-1" - transpose operations, inverse matrix calculation. All these are matrices (arrays) and must be programmed according to matrix algebra http://alglib.sources.ru/matrixops/
There are fragments of C codes but they need to be checked. Everything works in matkadel.
I don't know if I can do it at work, but it is a worthy task for a master, maybe in my spare time. The aim is maximum speed and accuracy of the calculation. Matrix H type integer (consisting of 0 or 1). The rest are double.
Or anyone who can handle it, just nod. I will try to write detailed step by step instructions (I have experience in MQL programming).
This means that 10-100 billion Kalman filters are working in parallel and each of them receives quotes. If the quote flow corresponds to the nested model, then everything is OK, we listen to news, trend, flat, etc. If there is no signal (discrepancy at the filter output exceeds threshold) all we have to do is to choose a filter out of the remaining 99 (billion-1) which best corresponds to the ongoing process (the model enclosed in it).
The main problem in trading - by the time the model is more or less reliably recognised, the probabilities of its continuation and collapse are about the same. I'm afraid this rule will apply to all 10-100-milliard Kalman filters.
This means that 10-100 billion Kalman filters are working in parallel and each of them receives quotes. If the quote flow corresponds to the nested model, then everything is OK, we listen to news, trend, flat, etc. When the signal disappears (discrepancy at the filter output exceeds the threshold) all we have to do is to look for a filter out of the remaining 99 (billion-1) which best corresponds to the ongoing process (the model embedded in it).
The main problem in trading is that by the time a model is more or less reliably recognised the probabilities of its continuation and collapse are about the same. I'm afraid this rule will apply to all 10-100m Kalman filters as well.
Well, I think that's an overly harsh statement. In fact, there are no studies that give statistics on the lifespan of models. Moreover, there is no data on the amount of information (=lag time) required to recognise a model. Even those who introduce and use these models prefer not to conduct or publish such studies. Obviously, it is believed that if the strategy has a positive mo, then the model is recognised before the probabilities are aligned.
And there are such strategies, live ones. Look at Better. His Expert Advisor actually does what I wanted to implement in mine - it recognizes the turning points and enters at the beginning of the wave. And it moves up as well as down. Here you have a forecast and the recognition beforehand.
As for Prival 's program I would say the following: it is interesting, there is an idea, the parallel is not so distant. Unfortunately I haven't understood mathematics, I have a lot of cases of my own, but if the transition matrix is not something fixed, there may be a solution on this way. But the computational part needs to be less sprawling. If only direct calculation process requires calculation over 10-100 billions of filters, then we can forget about ticks. And there is also the inverse problem, we must somehow adjust the parameters to changing market conditions.
So, it is necessary to clearly estimate resources both in terms of memory and computing cycle time. Otherwise we may get one calculation cycle of 5-10 hours. What will be the news then? All we will have to do is to play for days or weeks. :-)
There are variants of construction of adaptive F, to them proceed if parallel calculation of several filters exceeds in computational cost the adaptation. i.e. matrix F(t,ACF,L) depends on time, ACF parameters and L - some properties of flow. But this is already the domain of non-linear filtering. I would like to stay within the limits of linear filtration for now. Dial in statistics for ACF in typical areas (quiet market, session opening, news release, several trends with different parameters, several flutes with different parameters). As they say pull the strings to see. I think about 10-16 filters will be enough, when a discrepancy appears, divergence from the model, a decision should be made (critical point of the market - decision point). At this point switch to Wald statistical decision functions. Somehow, so far I do not have answers to all questions, only a clear path and a goal.
Yes about the detection time, it depends on the quality of the features and the set of models. It may be instantaneous. Example (let's say in the set) there will be 2 filters responsible for working with gaps (1 up 1 down). Selection from the whole set of models is unambiguous + the trait is quite powerful :-).