Discussion of article "Price series discretization, random component and noise"

[MetaQuotes]

New article Price series discretization, random component and noise has been published:

We usually analyze the market using candlesticks or bars that slice the price series into regular intervals. Doesn't such discretization method distort the real structure of market movements? Discretization of an audio signal at regular intervals is an acceptable solution because an audio signal is a function that changes over time. The signal itself is an amplitude which depends on time. This signal property is fundamental.

Attentive traders may notice that the candlesticks in the market are conventionally divided into groups of "large" and "small" sized candlesticks (areas with high and low volatility), which means that the chart is not a random walk and there are patterns. If time discretization introduced strong distortions, then this effect would not be observed. However, this feature can be explained by the fact that the candlestick size depends on the number of trading operations executed inside this candlestick. How this can be checked? You can simply look at the chart with tick volumes - "small candlestick" periods are accompanied by low tick volumes, and "large candlestick" periods come alongside high tick volume periods. If we assume that one tick is one step, then the price makes more steps during "large candlestick" periods, but the candlestick size remains proportional to the square root of the number of steps multiplied by the average step size (example on Figure 9). Tick volumes, in turn, are directly correlated with the trading activity: the higher the trading activity, the more ticks pass per unit of time. Exchange markets provide the history of real volumes, where you can see that tick volumes strongly correlate with real volumes, which also indicates the relationship between the number of ticks and the intensity of trading activity.

Figure 9.

This also proves that time discretization introduces strong distortions to the resulting price series form and thus it makes price analysis more difficult. This distortion has led to the emergence of a separate category of trading systems, the so-called "night scalpers". I am not saying that they cannot generate profits, but it is necessary to take into account this peculiarity of a price series presentation when developing such systems and to conduct additional research in order to answer the following question: "Is the probability of a reversal in these areas really higher than the probability of a trend continuation?" and "Do the statistical characteristics of these areas allow to generate a profit?", because such systems are based on this pattern. 

Author: Maxim Romanov

[Rorschach]

0.000141*(60^0.5) 0.000141*(1440^0.5) like 0.000170 is needed.

My results

The average of tics or m1 will vary from site to site, even with a lot of data. But in general, T^0.5 works more or less well, though at higher tf the error starts to grow.

If you make renges, you should probably take a larger spread, so that the tick size would be smaller than the renges. It is also possible to take the size of the rendering in 1 _Point and then make an equivolume chart with the second pass. There is a lot to experiment with.

[Maxim Romanov]

Rorschach:

0.000141*(60^0.5) 0.000141*(1440^0.5) like 0.000170 is needed.

My results

The average of tics or m1 will vary from site to site, even with a lot of data. But in general, T^0.5 works more or less well, but the error starts to grow at higher tf.

If you make renges, you should probably take a larger spread, so that the tick size would be smaller than the renges. It is also possible to take the size of the rendering in 1 _Point and then make an equivolume chart with the second pass. There is a lot to experiment with.

Yes, you are correct, I wrote the wrong data in the table, thanks.

About larger time frames. I have analysed more than 30 currency pairs, a couple of dozens of stocks, crypto and raw materials, and it turned out that on larger time frames it still tends to a normal distribution. But I did it differently, not as described in the article. Perhaps there will be deviations somewhere. And on stock markets the deviation is bigger than on currency markets, but it also depends on the instrument. On amd, appl and sberbank you can even make money on this deviation. I will write an article to show you where you can make money on it, and where the deviation is just enough to cover commissions.

[Igor Makanu]

In my opinion, what the author calls "Alternative variant of price series discretisation" is quantisation of time series with samples not linked to the time scale (just sequential number of samples).

[Maxim Romanov]

Igor Makanu:
in my opinion, what the author calls "Alternative variant of price series discretisation" is quantisation of time series with samples not linked to the time scale (just sequential number of samples).

Is quantisation different from discretisation)?

[Igor Makanu]

Maxim Romanov:
Is quantisation different from sampling?)

Yes, they are.

sampling is measuring the value of a signal at specific intervals of time

quantisation is dividing a signal into specific levels.

UPD: you can also do this:

- sampling is digitising a signal with a sampling rate ( on the x-axis )

- quantisation is digitising the signal into specific rigidly defined levels ( Y axis )

[Maxim Romanov]

Igor Makanu:

yes, they do

discretisation is the measurement of the signal value at certain time intervals

quantisation is the division of a signal into specific levels

UPD: you can also do this:

- sampling digitise the signal with the sampling frequency ( on the X axis )

- quantisation digitise the signal by specific hard-defined levels ( on the Y axis).

Yes, I agree, there is such a subtlety. I had an idea to write about quantisation, but I wanted as wide audience as possible to understand the essence. From my experience, many people far from science do not understand quantisation. After all, I was writing for traders and not all of them are friends with maths and physics.

[Реter Konow]

The first third of the article is a brilliantly simple and clear analysis of the nature of pricing.

The fourth point in the list - price as a function of itself - struck me. This is the apotheosis of trader's thought. Congratulations.

[Aleksey Nikolayev]

Реter Konow:

I was struck by the fourth item on the list - price as a function of itself. This is the apotheosis of trader's thought. Congratulations.

Autoregression, for example.

[Реter Konow]

Aleksey Nikolayev:

Autoregression, for example.

Consideration of the actual mechanism of price dependence itself, is the domain of practitioner researchers. A significant event in a trader's life is the point of philosophical understanding (and level of professional maturity), when he finds himself able to realise a regular and consistent market evolution, the last stage of which is the complete dependence of price on itself with the cutting of ties with the outside world.

This trader's wisdom is admirable.

I should add that during this so-called "market evolution" the price has been steadily losing discreteness, becoming more and more linear, and somewhere at the peak of self-looping and continuity there is a "rupture" of the semantic "shell" of the market process.

[Maxim Romanov]

Реter Konow:
The first third of the article is an ingenious parsing of the nature of pricing in its simplicity and clarity.

The fourth point in the list - price as a function of itself - struck me. This is the apotheosis of trader's thought. Congratulations.

Thank you! I plan to write about trends, it will be interesting.