Probability assessment is purely mathematical - page 13
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Unfortunately, I've got Win7 -64 and can't get the matcad on it. version 15 has already been released, but it won't work for me ((
http://rutracker.org/forum/viewtopic.php?t=3030331
Say Oracle VirtualBox will allow you to put a previous version of Windows on a working machine, and you can already put a matcad in it. It's easy to set up and use. I recommend using seamless mode - after starting the virtual machine, press the host key (normally the right control key) together with " L ", convenient.
Hint where this formula is taken from,
interval [-2/sqrt(n); 2/sqrt(n)]
I'm just curious, I think I calculated it differently, if need be I can dig around and find it.
I don't remember, you have to look it up. Saw it in an article.
2. It is a very realistic assumption that if we take a segment of history shifted 1 bar to the left (or right) of what we took in 1, the probability distribution will change very little.
For bars it depends on the number of ticks hit. I don't quite understand how it is averaged, etc., but there may be errors related to the fact that m15 bars have stable intraday changes in volatility (and consequently in increments). We should perform a more detailed analysis. Maybe it is not that simple.
Here is, for example, a similar study: we measure the average incremental length modulo m15 and h1 for example. For SB, according to Einstein's f-law the average body length h1 will be 2 times larger, in reality there are significant deviations for different periods as well. But again, we need to analyse the increments that do not have a systematic difference in volatility - for example, to average for each hour separately, or to take the timeframe of the day and above.
But I would argue about differentiation: each differentiation operation nullifies one order of dependence, if represented polynomially.
A profound misconception. My suspicions about your indicator were intuitive and wrong. The indicator is most likely correct, but the use of it is methodologically incorrect.
What does your indicator (ACF BP) show? That there are dependencies in BP. Sorry, but this is a platitude. No one is denying the presence of trends and so it can be seen without any mathematics. Moreover, it is not correct to investigate the regular components of BP by methods of mathematical statistics. Your post has once again convinced me of the need to stick to software packages - this will avoid methodological errors. In our case we need to exclude the regular components - trend and cyclic component, if we want to see in BP what is not visible to the naked mathematical eye.
What do we want to see? We want to see the parameters of a model, by which we could not only analyse historical data, but also predict the future. This is what the ACF of differences, difference-in-differences, etc. are built for. For example, when identifying the ARPSS model we initially get two possible answers: the model can be identified and the model cannot be identified. Please agree that this result is already worthy of taking differences, and your arguments about loss of information are groundless, since we exclude an established fact (t rand) from consideration, and try to obtain information that is not initially visible at all.
It can only be done by analysing ticks, bars won't do. But that's just my opinion...
It's not the first time I've seen your opinion on ticks. In my opinion ticks statistics has nothing to do with timeframe statistics, and each timeframe has its own statistics, and one is not deductible from the other. It is deducible at the level of analytical indicators, not statistics.
As a proof I propose two pictures. EURUSD30 has 7200 bars on one of them. On the other one, EURUSD60 is 3600 bars. We have different Fourier decompositions!
I deliberately took close timeframes.
A profound misconception. My suspicions about your indicator were intuitive and wrong. The indicator is most likely correct, but the use of it is methodologically incorrect.
What does your indicator (ACF BP) show? That there are dependencies in BP. Sorry, but this is a platitude. No one is denying the presence of trends and it can be seen that way without any mathematics. Moreover, it is not correct to investigate the regular components of BP by methods of mathematical statistics. Your post has once again convinced me of the need to stick to software packages - this will avoid methodological errors. In our case we need to exclude the regular components - trend and cyclic component, if we want to see in BP what is not visible to the naked mathematical eye.
What do we want to see? We want to see the parameters of a model, by which we could not only analyse historical data, but also predict the future. This is what the ACF of differences, difference-in-differences, etc. are built for. For example, when identifying the ARPSS model we initially get two possible answers: the model can be identified and the model cannot be identified. Please agree that this result is already worth taking differences, and your arguments about loss of information are groundless, as we exclude an established fact (t rand) and try to get information that is not initially visible at all.
As for the hypothesis of randomness or non-randomness of BP - I, personally, prefer the geometric Brownian Wandering model with drift, where the value of a rather broad moving average (e.g. 200 period) is used as the drift.
If you then look at the differences from that average - you can get curious results about the distribution...
;)
I am going to put in my own penny. I will not give a general proof, I will demonstrate a simple experience. We take an arbitrary point in time and calculate the distribution of increments, for example, for 10 minutes (we are on M1). It is not exactly symmetric, it is the effect of a global trend for the analyzed period.
In the upper left corner, integrals for the positive and negative halves of the distribution are given, they are 0.503 and 0.497.
Now, we complicate the condition and take increments only if price moved negatively in the previous 10 min and not less than 5 points. It turns out that this condition significantly deforms distribution. I will not show any pictures; the integrals become 0.5135 and 0.4865. That is, the probability of a positive move has become higher.
If we set not -5 but +5, we obtain 0.4439 and 0.5561, now the probability of negative movement has increased (much more significant).
In other words, we can clearly see the effect called market reversion.
Alas, a simple calculation shows that even 1 old point spread completely kills this effect, i.e. makes it unusable for making profit.
If you accept the current price movement as derived from macroeconomic news or speculative trends, then I suggest you simply recalculate (1,2,3, ....) the number of factors and complex (terribly complex) intricacies in the form of constant overlay of one news on another, echoes from one market to another and other, idiotically innumerable events that affect the current price position. If you are happy to "conserve" statistics and use them (literally) as a basis for proving the long-term trends of the market? Then everything is a standard statistician's approach, which is wishful thinking.
How can one look at the enormous number of superimposed factors, which allegedly drive the market, and then base a long-term plan on that ...........? HOW? What evidence are you talking about?
I've written this here before, but I'll say it again ........
Phantoms we create:
may the army of "elioters" forgive me, but the adherence to the technique of identifying waves, bouncing off levels and the principled expectation of passing through psychological levels with .0000 (zeros) after the decimal point, is nothing but mass worship of an odious idea. But at the expense of the massiveness of this worship, technically this model has a place. And that's great. But how is it different from reading coffee grounds? And how can a confidently lagging indicator, or rock-painting on the historical traces of quotes, help in this case?
I assess everything that happens as a primitive upward and downward price movement. And that is enough for me, especially since it is an absolutely repeatable phenomenon. The calculation of probability of results (link to the topicstarter) with the same starting conditions will steadily tend to the value of 50/50 for a period. And this trend is also absolutely systematic.
Events (price movements) in the past are nothing more than statistical data having a visual representation, I am disinclined to consider historical moving averages tied to price changes in the present. If only because extracting precious regularities from such practices is akin to self-delusion.
The incalculable number of superimposed factors pushing something in this world stabilizes and simplifies it to an abomination. The incalculable number of electrons and protons in your body does not prevent your body from being stable. God forbid, if there are more electrons than protons, your body ceases to exist.
A more complicated example. Light from the Sun flies to us in a straight line only because it undergoes an incalculable number of interactions (pushes) at each of its steps. If there were no single interaction, the Sun's light would pour down on us from everywhere.
The incalculable number of interactions with no exceptions indicates a cumulative zero effect, which reduces the construction of the plans to a primitive - your body, be it may, does not suddenly disintegrate, and the light from the Sun around Mars does not circle before reaching us on Earth.
Alas, the lyrical "incalculable number of factors" does not apply to price movement. The primitive price movement up and down is due to a very few factors otherwise the price would move in a straight line to the speculative level with the minimum potential or take it instantly. There are relatively few price changes during the day as a result of transactions. Price movements are due to a small number of factors. Which makes it difficult for everyone. You see? If there were innumerable trades, we could neglect their zero effect and never think about it, as we do not think about the electric charge of our body or how the sun shines. But there are not many trades, so the price goes up and down depending on the difference in the sentiment of the dealers, which is comparable to the size of the sentiment itself. It's not difficult to build a model with sentiment that will generate a price that steadily tends to a 50/50 value in a period, but by knowing the sentiment, you get to make plans for the future.
In a nutshell, such a simple sentiment model can explain:
1) why price is moving UP and DOWN;
2) why price tends to 50/50;
3) how, knowing the sentiment, you can make a profit.
I doubt you were building a model with "innumerable factors" or anything like that. More likely you trusted your intuition. But imagine that there are models that explain price behaviour. And for example, in order to argue that within the above model price is absolutely random, you would need to show that the difference in sentiment is absolutely random, that yesterday's prevailing desire to buy has no effect on today's. To do this, with a bit of work and synchronising the model with the real market, you will get a confirmation answer - the sentiment is absolutely random. Or you won't.
It's not as simple as it sounds. Elioters or moving averages are just an add-on to price. It's easy to accuse them of self-delusion as they juggle the consequence. Try addressing the cause, looking underneath the price, so to speak.
Do you believe that the trends and cyclical components you have identified have the right to be considered as such in the future?
In a stationary market, yes. In a stationary section of a non-stationary market, yes.