Obtaining a stationary BP from a price BP - page 21
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Sergey, I find many conceptual "inconsistencies" in your approach. On the one hand you say that stationarity is impossible, and on the other hand you assure that statistically the system stays stable for about a month (no parameter changes required). But in that case, who prevents you from adjusting the parameters to stationarity once a month?
Hello, Sergei.
No one's stopping me. That's what I do.
Predicting by one countdown is a dead end. A time lag of one count is total Chaos, you can never predict anything there.
In the limit, "optimal" trading comes down to a rollover strategy and being in the market all the time. Indeed, when we don't know what to do (which way to open a position), it is considered appropriate to sit on the fence and smoke bamboo. However, if we analyze the situation, we have to pay a commission in the form of spread for "doing nothing". Technically, "doing nothing" means an equal outcome for long/short positions, hence there is no point in closing the current position - you have to wait for a signal to reverse. Thus, the entire BP price is broken down into non-equidistant segments, the direction of which should be predicted in terms of the "optimal" strategy.
It turns out that predicting just one step forward is important, and it makes absolutely no sense to predict for 2 or more steps. But this is certainly true within the "optimal" strategy defined in this way, from the point of view of any other TS the prediction can be anything else. Including a multi-step one.
Oh how!!!! And you write that you don't see the feasibility of bringing it to stationary? But let me see, what you are doing x(n)-x(n-1) is not one way of bringing a series to stationary?
I don't!
The first-difference series (FDR) from the price series is not stationary in any sense. It has the most unpredictable MO (though around zero), forcing us to "see" an uptrend in the price GP, when MO ROD>0, and a downtrend when MO<0 and a flat when MO->0. It has a standard deviation (volatility) with a daily period. I don't understand why and how do we need to restate it? Do we want to get from it a SV with normal distribution with zero MO and variance equal to a constant? Even if we get it by some unknown method, what do we do with this "miracle"?
As for your autocorrelation pictures, I will not comment on them.
FOXXXi wrote(a) >> Do you think Reshetov is such a dumbass that he confused the first difference with the cumulative sum - you call it integration.
No, I don't think so.
But I am sure that Reshetov does not need defenders and can say himself what he does and why he does it.
What I meant is if we obtain a stationary series (white noise) then its first differences are unpredictable because the ACF=0 but the cumulative sum of white noise itself is predictable.
to Yurixx
Yura, hello!
And you, if memory serves me correctly, are the Father, Son and the Holy Spirit of the idea of restification (or, bringing to a normal form) of RPR from the price VR. Maybe you can give voice to the basic idea. Will you put order into my inflamed mind?
In the limit, "optimal" trading comes down to a rollover strategy and being in the market all the time. Indeed, when we do not know what to do (which way to open a position), it is considered appropriate to sit on the fence and smoke bamboo. However, if we analyze the situation, we have to pay a commission in the form of spread for "doing nothing". Technically, "doing nothing" means an equal outcome for long/short positions, hence there is no point in closing the current position - you have to wait for a signal to reverse. Thus, the entire BP price is broken down into non-equidistant segments, the direction of which should be predicted in terms of the "optimal" strategy.
It turns out that predicting just one step forward is important, and it makes absolutely no sense to predict for 2 or more steps. But this is certainly true within the "optimal" strategy defined in this way, from the point of view of any other TS the prediction can be anything else. Including a multi-step one.
There is a deep philosophy here. What is primary, the prediction model and consequently building the TS on its basis or the TS for which the prediction is selected. I do not really understand what the "optimal" TS means (on what range, among what this optimum is), why only one step forward is important for it, how it correlates with spread. If it's a long story, then you don't have to.
I can't see it!
The first difference series (FDR) from the price series is not stationary in any sense. It has the most unpredictable MO variation (though it is near zero), forcing us to "see" an uptrend in the price GP, when MO ROD>0, and a downtrend when MO<0 and a flat when MO->0. It has a standard deviation (volatility) with a daily period. I don't understand why and how do we need to restate it?
I didn't say that this series is super stationary, but it passes some stationarity tests. It's important to understand what this series is used for. If you use it for forecasting with the known methods, it won't be correct, because the distribution doesn't correspond to the normal one at all and will always cause the "increased" error.
Do we want to get from it a SV with normal distribution with zero MO and variance equal to a constant? Even if we obtain it by some unknown method, what should we do with this "miracle"?
I wrote, - it gives you the opportunity to apply the tried and tested maths where it makes sense to apply it :o)
As for your pictures of autocorrelation, I won't comment on them.
Don't comment, (I don't know how to portray the "shrug" emoticon). If you mean absence of 1 on zero count, sorry, forgot to remove my conversion (implemented simply in one function, this preparation of row to pass to next algorithm). I'll recalculate it when I have time, but conceptually it's approximately the same.
Do your parents know what you do on the internet here?
Is the question for everyone or for specific people? :о)
It turns out that it is one step ahead that matters, and it makes absolutely no sense to predict 2 or more steps ahead. But this is of course true within the framework of the "optimal" strategy defined in this way, from the point of view of any other TS, the prediction can be anything else. Including multi-step.
+1
This is not true. The cumulative sum of normally distributed SV with MO=0 (white noise) is not predictable (in the sense that it is a martingale and therefore impossible to make money on it)!
If the cumulative sum deviates from MO by two sigmas, with 97,5 % probability it will return there again, irrespective of sampling frequency, be it ticks or oscillators. For example we can enter at one sigma, there will be more trades, but probability of return will be 67 %, and in 33 % case it will go to two or three sigmas.In fact if a stationary process deviates from the MO by even a small amount it will return to its MO with 100% probability,because this is the "fair price" of this process.This is a kind of attractor to all sorts of non-linear dynamic systems lovers.
If the cumulative white noise deviates from the MO by two sigmas, there is a 97.5% probability that it will return there again regardless of the sampling rate, be it ticks or oscillators.For example we can enter at one sigma, there will be more trades, but the probability of return will be 67%, and in 33% case it will go to two or three sigmas. In fact, if the process deviates from MO at least by one sigma, it will return to its MO with 100% probability, because this is the "fair price" of this process.
Neutron wrote >>
2."white noise is unpredictable by definition, BUT (that) will still be able to trade profitably in it" - a logical contradiction!It is. MO is Fair Value stationary BP and one can always trade (play) on the rebound from the channels drawn by the SCO - a return to MO is guaranteed.
Generate a series according to any of your requirements - white or any other noise. For example, minutes. Let's change that every Thursday at X hours with a deterministic dependence - any, for example, that if the previous minute candle is black, then the next hour will be shifted down by Z points. We analyse the changed increments - all the same noise. But it is not a real profit, it is a real grail)))
What is it, R/S analysis - timing, or "dependence" on days of the week, hours, etc. Don't need details, general concept.
If the cumulative white noise deviates from the MO by two sigmas, there is a 97.5% probability that it will return there again regardless of the sampling rate, be it ticks or oscillators.For example we can enter at one sigma, there will be more trades, but the probability of return will be 67%, and in 33% of cases it will go to two or three sigmas. In fact, if the process deviates from the MO any way, it will return to its MO with 100% probability, because this is the "fair price" of this process.
Sorry, but that's not true again. The increments are independent and nothing should go back anywhere. How does the cumulative amount go back to the mo? Take SB with increments with mo=0 - it can deviate from zero as far as it wants and not return to it as long as it wants. The cumulative sum has a variance that increases in direct proportion to the square of time.
I do not understand what you have written here, it is understandable why. What is it, R/S analysis - timing, or "dependence" on the days of the week, hours, etc.? Do not need details, the general concept.
It's an elementary example of how to mix in a series of any deterministic dependence and show that the series will retain all the properties for which you believe it is unpredictable.