Discussion of article "Probability theory and mathematical statistics with examples (part I): Fundamentals and elementary theory" - page 3
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but for practical purposes, you need to be able to evaluate a trading strategy in the future, not forecast a price series
Igor Makanu:
the outcome of these studies will be either the price is random in nature or there are patterns (in history), here you have it "on a platter"!
Randomness and unpredictability are different things (with mathematicians). We need to come to a common terminology, otherwise the discussion of the article will slip into arguments about terms.
There are two extreme cases - a completely regular process (sinusoid, for example) and a completely unpredictable one (random walk).
The price is between them (in mathematicians it is called "random process", i.e. predictable with some probability).
Frankly speaking, I consider the approach related only to forecasting to be insufficient (due to the inherent non-stationarity of the market). It should be supplemented with an approach related to the definition of the breakdown(the moment of change of model parameters).
My experience says that models with constant parameters (or piecewise constant ones that need to be changed sometimes) do not fit the market very well.
The question is rather about the theory of building scientific models. Where to get ideas, what formulas to use for modelling, how to assess the quality of the model, and there forecasting, discord.
The question you raise is somewhat immense. For example, the criterion of scientificity is one of the basic questions of philosophy, which still has no clear answer. All simple methods (like Popper's principle of falsifiability) are unsuitable because they do not answer themselves and turn out to be unscientific by their logic.
If we confine ourselves to the theorist, there are several basic "building blocks" from which probabilistic models are constructed and ways to test them. The most basic, perhaps, is "a sequence of independent identically distributed random variables" - will be in the second article. Also important are the "maximum likelihood principle" and"hypothesis testing" - I've talked about them in this article. For example, my article about gaps used two "blocks" of these three (the first and the third).
Actually, I see my task in this series of articles as an attempt to tell about the main "building blocks" in a coherent and not too complicated way (but not distorting the essence by simplification).
Randomness and unpredictability are different things (for mathematicians). It is necessary to come to a common terminology, otherwise the discussion of the article will slip into arguments about terms.
Let's talk about terminology
if we are talking in the context of price prediction, then we must necessarily take into account the reliability of the prediction
how will the forecast error be evaluated?
1. is it the maximum deviation of the price from the forecast ?
2. is it the time during which the forecast will be valid ?
3. is it item 1 + item 2 ?
Trading is price prediction. You may not like the term, but that's essentially what it is. Simplified, you need to enter a trade for 1 bar, and before entering you give a prediction - up or down. You make a prediction (implicitly) that your trade will be profitable, otherwise you would not have opened it.
On the next bar the trade is closed, and you can evaluate the quality of your forecast (aka the quality of the trading system).
it won't work like that
Let's discard capital management, although it is a significant part of the TS.
for trading it is important not only to forecast where the price will reach, but it is also important to assume when it will happen, or it is necessary to take into account what happened before the moment of market entry, i.e. it is necessary to analyse a certain set-up or pattern.
but just to make a forecast that the price will break such and such level... Well, everyone does it on thematic forums, but rarely these forecasts help to earn money.
I agree if you assume a forecast for one bar and every bar to close and open a deal, but such TS will work on TF D1 and above.
Ilyinsky tells a lot of interesting things about what banks have been doing in the past 10 years. Mostly about options, but there is also a bit about other things. But there are a lot of formulas, I would like to see them in an easier format.
43 minutes
Other lectures.
Isn't that the same thing?
Continuous time can be reduced to discrete time by discretisation. Discrete time can be reduced to continuous time by interpolation (but nobody needs this in practice, because the tools for analysing the world around us (deduction techniques) are discrete).
Sometimes it is easier to calculate for processes with continuous time. For example, the Black-Scholes formula. Of course, it does not describe everything exactly, but it is useful to know it at least to understand the essence of the notorious "Greeks".
My experience says that models with constant parameters (or piecewise-constant parameters that need to be changed occasionally) don't really fit the market.
I'd love to read an article describing your approach)
The problem with constant and piecewise constant models is that we can't not use them) In fact, the approach using Expert Advisors that are optimised or re-optimised is the use of this approach. And only the freedom and creative flight of manual trading allows us to avoid these models)
Randomness and unpredictability are different things (with mathematicians).
To be honest, terms like "random event" or "random process" in the theorist do not mean that the concept of "randomness" is defined or revealed there in any way. The notion of unpredictability is not particularly mathematical either.
Ilyinsky tells a lot of interesting things about what banks have been doing in the past 10 years. Mostly about options, but there is also a bit about other things. But there are a lot of formulas, I would like to see them in an easier format.
43 minutes
Other lectures.
Yes, I am familiar with this lecture. The presentation is intriguing and engaging, but poorly understood due to the complexity of the subject. There's some pretty complex maths at the heart of it - fractal Brownian motion etc. I don't yet understand how to put it into a popular form.