The market is a controlled dynamic system. - page 62
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But if you do intermediate filtration, as you should.
Nothing should be done, duh. If you deliberately trim the derivatives, you get trimmed derivatives, no surprise there. And if you don't trim, you get uncircumcised.
And it would be a dead end to throw out freezing information just to bend the system to your own analysis methods - especially for a trading system: we need to get reliable real-time signal information, while filtering introduces a group delay and also cuts off the high-frequency half of the pulse spectrum - the very half that provides a good detectable edge.
In short, after smoothing you can detect a signal as much as you want and even find it reliably, but this information is practically worthless at the moment of obtaining it. That is why I am categorically against any kind of pre-filtering, we should work with clean quotes.
Nothing follows, duh. If you purposely trim the derivatives, you'll get trimmed derivatives, no surprise there. And if you don't trim, you get uncut.
And it would be a dead end to throw out freezing information just to fit your own analysis methods - especially for a trading system: it's important to get reliable real-time signal information, while filtering introduces a group delay and also cuts off the high-frequency half of the wavelet spectrum - the very half that provides a good detectable edge.
In short, after smoothing you can detect a signal as much as you want and even find it reliably, but this information is practically worthless at the moment of obtaining it. That is why I am categorically against any kind of pre-filtering, we should work with clean quotes.
Well, you shouldn't, so you shouldn't... This is your point of view. And I am not going to argue with it.
But in this case it is not correct to talk about derivatives.
data for the first 10 EURUSD derivatives:
This set of numbers are NOT derivatives!
Taylor's series on differences d1, d2, ... d8.
GBPUSD Daily
1) without intermediate difference filtering
2) with intermediate difference filtering
That is, sort of like the percentage of the marks that are guessed... it's a thankless task, it seems to me... can't get out from under the noise here, have to work within 50-55% somewhere. I'll keep that in mind though.
No, sum up the increments in the direction of the forecast and separately in the opposite direction. Dividing one by the other is the profit factor formula. Not only the % of guessed signs, but also the magnitudes of the increments themselves are taken into account
This indicator simultaneously takes into account not only the prediction error but also the guessed signal. I.e. essentially signal/noise in DSP terms (I guess))) as I'm not familiar with DSP). And it doesn't require HP of prediction error, like estimation via error cramp, etc.
Regarding how the error should be distributed. I don't think it matters either) I can see why econometricians want the error to be white noise: zero mo - no trend in the error, finite variance - the error does not grow to unpredictable sizes rendering evaluation of the useful signal (deterministic component) meaningless. But it hasn't come to the trades yet. A simple stop loss setting is able to cut off unwanted tails and limit the variance of the return distribution of the trade. I.e. as long as the noise can be anything as long as it doesn't interfere with the criterion of model quality evaluation. If the estimation of signal/noise is all the same before the signal and noise distribution, we can estimate the model qualitatively, and that's all we need at this stage. imha
And one should not consider error in the classical sense as a difference between forecast and reality, but take into account the direction of error. Immediately go to the trader's real, where an error in the right direction is not an error but a profit)). I.e. if the forecast - growth of 40 points, and it grew by 100, then don't judge the model strictly) For example, trend following is based on such errors - ejections in the right direction. They cut off the distribution of increments in the loss-making zone with a stop-loss and catch rare spikes in many sigmas in the right direction without taking a take-profit. And if you look at the distribution of returns, it is far from normal, as is the distribution of error. The proposed PF formula takes this into account.
Taylor's series on differences d1, d2, ... d8.
GBPUSD Daily
1) without intermediate difference filtration
2) with intermediate difference filtration
1. You just proved that if you cut the higher derivatives it will approximate the Taylor series. That's obvious to the hedgehog. Eventually it's possible to filter the quotes to the extent that they will even turn into a straight line, so what's more fun then? We are interested in the original series, and only that.
2. These gimmicks are useless in practice, I repeat, because of the delay they introduce. We are not dealing with function approximation, but with real-time detection and prediction. In your picture you can see that the filtered signal lags, and this is unacceptable, because the decision to enter the trade should be made here and now, and it will be too late in the next readout. That's why the only variant is the anticipatory forecast based on local regularities detection by non-linear methods and non-linear criteria, which would show, how well we guessed the current structure and system parameters.
In our case, the problem of synthesizing optimal control is non-standard, so the tricks described in books on electronics and radar are mostly unsuitable.
No, sum up the incremental values in the direction of the forecast and separately in the opposite direction. Dividing one by the other is a profit factor formula. Not only % of guessed signs, but also the values of increments themselves are taken into account
This figure takes into account not only forecast error but also the guessed signal. I.e. essentially signal/noise in DSP terms (probably))) since I'm not strong in DSP). And it doesn't require HP of prediction error, like estimation via error cramp, etc.
Regarding how the error should be distributed. I don't think it matters either) I can see why econometricians want the error to be white noise: zero mo - no trend in the error, finite variance - the error does not grow to unpredictable sizes rendering evaluation of the useful signal (deterministic component) meaningless. But it hasn't come to the trades yet. A simple stop loss setting is able to cut off unwanted tails and limit the variance of the return distribution of the trade. I.e. as long as the noise can be anything as long as it doesn't interfere with the criterion of model quality evaluation. If signal/noise estimation doesn't matter before signal and noise distribution, we can estimate the model qualitatively, and that's all we need at this stage. imha
All this is true only if we consider a system that constantly predicts and makes trades. But it does not fit the case when the system detects the optimal entry points, where in its opinion a high-quality forecast is possible, and only then selects a forecast direction. In practice there may be 2-5 entries per week on a minute chart, i.e. the number of made forecasts is less than 0.1% of the number of octivation samples.
And the error should be considered not in the classical sense as the difference between the forecast and reality, but in the direction of the error. Immediately go to the traders' real, where an error in the right direction is not an error, but a profit)). I.e. if the forecast - growth of 40 points, and it grew by 100, then don't judge the model strictly) For example, trend following is based on such errors - ejections in the right direction. They cut off the distribution of increments in the loss-making zone with a stop-loss and catch rare spikes in many sigmas in the right direction without taking a take-profit. And if you look at the distribution of returns, it is far from normal, as is the distribution of error. The proposed PF formula takes this into account.
Heh, it's certainly tempting, but the right error-returns happen AFTER we've bought. And we have to evaluate the criterion and determine the direction BEFORE entering. So, if we know BEFORE entering that an outlier to one side is more likely than an outlier to the other, we can simply factor that into our system, and use it henceforth.
Also, I was wrong to erase the diagram along the way: there were TWO errors drawn on it: 1) internal modelling error, about which I said it should be normal and uncorrelated, as it is a criterion that the model adequately describes the system structure(econometrics has nothing to do with it), and 2) prediction error, which should not and will not be normal, as the input has those very unpredictable abnormal outliers. And this is even a good thing, because otherwise even our potential earnings would probably be guaranteed to be 0.
but okay... I'm not going to change your mind... Suit yourself...
But it seems to me that you are not familiar with the task of optimal control synthesis - I'm not referring to the tester "optimizer" here.
Taylor's series on differences d1, d2, ... d8.
In order to apply a Taylor series expansion, the function must be infinitely differentiable.
However, various random walks (including those with high order unpredictable moments) are not differentiable. And prices are quite similar to random walk :)
In order to apply a Taylor series expansion, the function must be infinitely differentiable.
However, various random walks (including those with unpredictable high order moments) are not differentiable. And prices are quite similar to random walk :)
Quite right. That is why we should not talk about derivatives, but about increments. Proximity of the obtained increments to derivatives can be estimated using Taylor series by formally substituting the obtained increments for derivatives which appear in Taylor series. The resulting estimate of the series indirectly indicates the quality of the approximation.