What makes an unsteady graph unsteady or why oil is oil? - page 27

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to gpwr.

Тоже рад с Вами здесь встретиться. По прежнему на работе пытаюсь создать "мыслящую сеть" близкую к мозгу используя спайки и время. Но пока кроме простого распознования обьектов ничего не получается. Многие сомневаются что спайковые сети обладают каким то преимуществами по сравнению с обычными нейронными сетями. Но это тема отдельного разговора.

Yes, that's a whole separate conversation.

to timbo

The first price difference is not stationary.

It depends on what you mean. :о) In a broad sense it's rather stationary (at least for the main distribution parameters - the mean and probably variance), since it passes some important tests. But the stability of ACF with respect to shifts is a real problem, i.e. in the narrow sense it's not stationary at all. Although, there is no absolutely clear, unambiguous and objective criterion, so one can interpret "accuracy" any way one wants.

 
faa1947 >>:


На 16 стр. я приводил спектры для М1 и Н1 для одинакового временного интервала - 480 часов. Спектры принципиально разные. Вид спектра хорошо соответствует физике процесса. За 1 час началось и закончилось много трендов на М1, что соответствует инвесторам с разным временным горизонтом. Это пожалуй основная причина нестационарности ВР. Ваше утверждение совершенно должно бвыть справедливо для стационаных рядов, разлагаемых по Фурье.

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Ниже этой частоты спектры одинаковые. Нужны ли эти ВЧ детали? Если энергия того что отбрасывается довольно значительна?

Существуют методы усреднения СПМ. При этом, если существующие пики мало отличаются от среднего, то это флэт. В трендах основная мощность должна быть сосредоточена в пиках.

You shouldn't like cats...

First you have to prepare the senior taimfraim properly.
Then you have to calculate the spectrum correctly.
 
timbo >>:
Первая разница случайного блуждания - это неторгуемый процесс, торгуемый процесс само блуждание. Именно поэтому знание того, что первая разница стационарна, никак не поможет в торговле.
I get a similar feeling. I'm not so categorical, it's just not obvious to me that the first difference can be used.
 
timbo писал(а) >>
I was asking for a tradable process which would be white noise. The first difference of a random walk is a non-tradable process, the tradable process is the walk itself. Which is why knowing that the first difference is stationary will not help in any way in trading.

To put an end to the claim that the first price difference is stationary, I have written the enclosed stationarity test indicator in the broad sense. It works like this

  1. The differences of all prices are calculated
  2. The data is divided into two equal sectors
  3. In the first section, the first moment is calculated (the average of all prices in this section)
  4. From all prices in both sections, subtract the first moment calculated in step 3. It is clear that the data in the first section will have a zero average.
  5. Again the second moment (dispersion) is calculated on the first plot.
  6. The prices of both plots are divided by sqrt of the variance calculated in item 5. It is clear that the data on the first plot will have unit variance.
  7. We calculate the first and second moments of the prices in the second section and plot them as an indicator. If the data is stationary in the broad sense, then we expect that these moments will fluctuate around 0 and 1 respectively.

Calculations on EURUSD H1 show that the first momentum (average) does fluctuate around 0, but the second momentum (variance) increases from 1 to 3.4. So here it is difficult to call the price difference a stationary series even in the broad sense.

It is also interesting to check how close the price difference is to white noise. By definition, white noise has a flat spectrum. The definition says nothing about this noise having a normal distribution, though in most cases it is implied. My previous post has shown the ACF for the EURUSD H1 price difference. It has the form of a delta function. If we take a Fourier transform of the ACF, we get the power spectral density of the price difference, which is close to flat, i.e. the price difference is indeed close to white noise in a spectral sense. But in terms of the probability distribution, this is different. If we calculate the moments of price difference we will get the following table

Momentum Norm spread EURUSD USDJPY EURGBP USDCAD EURJPY
m4=E{x^4} 3 14.73 18.85 18.53 14.94 19.33
m6=E{x^6} 15 1090 2129 1320 962 1839

In all cases, the data are normalised so that their mean is zero and the variance is 1. As we can see from the table, the first variance of currency prices has much larger 4th and 6th moments than Gaussian noise (2nd moment equals 1 and all odd moments equals 0). In other words, the probability of detecting spikes greater than the variance is much higher for the price difference than for the Gaussian noise.

What does it all give us for trading?

  1. The ACF of the first price difference is a delta function, i.e. the correlation of the current difference to the past difference is close to zero. I don't see how such a process can be predicted.
  2. The first price difference is not stationary even in a broad sense. Therefore, I think trading based on the fact that the statistical behaviour of the price difference is constant over time is not profitable.
  3. The first price difference has large outliers beyond the variance which will lead to rapid reversals if positions are opened in the direction of the price difference returning to zero.

All codes used in my calculations are attached.

What statistical properties should prices have to be able to be predicted or traded profitably?

Files:
indicators.zip  2 kb
 
TOV >>:

Не выйдет. Я раньше тоже страдал ересью, писал заметки как представленная ниже.

What is your point?
 
begemot61 писал(а) >>
What's your point?

You won't predict more than half a period.

 
gpwr >>:

У меня такой вопрос ко всем участникам этой ветки: Какими статистическими свойствами цены должны обладать, чтобы их можно было предсказать или прибыльно торговать?

The first and most obvious is the constancy of the mean + the lack of "fat tails" in the distribution. In this case, nothing needs to be predicted.
 
TOV >>:

Вы не предскажите больше чем пол периода.

So you haven't shown anywhere what can be predicted at all.
I generally don't understand why it is considered by many to be possible to predict BP.
 
begemot61 писал(а) >>
First and most obvious, constancy of the mean + no "fat tails" in the distribution. In this case nothing needs to be predicted.


Are you talking about price or increments?

 
begemot61 >>:
Первое и самое очевидное, постоянство среднего + отсутствие "толстых хвостов" у распределения. В этом случае не требуется ничего предсказывать.

The first moment is already a constant and zero. The variance should not depend on time, and forget about "fat tails".
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