What makes an unsteady graph unsteady or why oil is oil? - page 33
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Каждая реализация помноженная на вероятность данной реализации равно мат.ожидание равно сегоднящней цене или нулю, смотря какая точка отсчёта. Для формулы x(t) = x(t-1) + e(t) мат.ожидание будет равно E[x(t)] = E[x(t-1)] + E[e(t)], где E[e(t)] = 0. Соответственно, E[x(t)] = E[x(t-1)]= E[x(t-2)] = E[x(t-3)] для любого t вплоть до того момента когда цена тебе уже известна и равна не мат.ожиданию, а конкретной цифре.
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Look, I've already written that I'm not going to argue about it. My opinion is that the series of quotes x(n)-x(n-1) is stationary, in the sense that the main distribution parameters are preserved. Or otherwise, their fluctuations can be considered stationary(on different scales). The ACF on a shift is not. I also wrote above about the necessity to study the behaviour of more segments (you read carefully):
That's the point that clear (to me) and proven verification methods require for some reason a larger number of segments, it simply requires a series. The obtained series of parameters by segments is analysed for consistency with a certain (depending on the method or its variant) distribution and only after that one can apply the trend criteria. It is difficult to draw such conclusions for two points.
Which is actually what I did a few years ago. This was confirmed by stationarity tests - normal statistical tests. If you believe that series x(n)-x(n-1) is not stationary, then there is also nothing wrong with it.
By the way, why did you cite it? Firstly, I've read it, and secondly, it doesn't contradict what I've said. By the way, the construction x(n)-x(n-1), ln(x(n)/ln(x(n-1), ((1/n)SUM(x(n)) are very well described by Shiryaev and he recommends them for reducing the series to stationary (I will not give screenshots, the book is in paper form).
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Я только хотел сказать, что приведенная мной методика проверки ряда на независимость приращений дает практически однозначный и теоретически на 99,99% обоснованный результат - ценовой ряд не является рядом с независимыми приращениями (даже если они мало или вообще не коррелируют). А это, в свою очередь, говорит о том, что все модели работы с ценой, подразумевающие независимость соседних отсчетов - неадекватны.
Более того, по-видимому (хотя это еще и надо доказать - а для этого просто не хватает исторических данных), статистическая зависимость между соседними отсчетами одинакова по форме на графиках ряда, по крайней мере, нескольких младших таймфреймов (вплоть до Н4 я это проверял с достаточной точностью). Т.Е. похоже на то, что указанная зависимость - явление неслучайное, как минимум, отчасти - а значит может быть спрогнозировано.
Еще раз повторюсь - этот вывод теоретический и основан исключительно на математике, никаких домыслов из области "фундаментального анализа":)
A powerful statement, and the main thing is that everyone subconsciously wants it to be true.
Indirect evidence of "non-random" price series increments is positive results in the market with NN. A random series (any random series) cannot be approximated, neither the series itself, nor its increments, nor the latent regularities of the series. If it is not, then it (the series) is non-random and has intrinsic regularities.
And it's probably time to stop with the "accidents" on the markets and discussing the characteristics of MF. The whole forum is already littered with such impractical arguments.
Look, I've already written that I'm not going to argue about it. My opinion - a series of quotes x(n)-x(n-1) is stationary, in the sense that the main distribution parameters are preserved. Or otherwise, their fluctuations can be considered stationary(on different scales). The ACF on a shift is not. I also wrote above about the necessity to study the behaviour of more segments (you read it carefully):
Which I actually did a few years ago. It was confirmed by stationarity tests - normal statistical tests. If you believe that the series x(n)-x(n-1) is not stationary, then there's nothing wrong with it either.
By the way, why did you cite it? Firstly, I've read it, and secondly, it doesn't contradict what I've said. By the way, construction x(n)-x(n-1), ln(x(n)/ln(x(n-1), ((1/n)SUM(x(n)) are very well described by Shiryaev and he recommends them for reducing series to stationary (I won't give screenshots, the books are on paper).
Well, if you read it, it has been mentioned many times that volatility has a memory - a dependence on previous values. Stationarity implies that the variance is independent of previous values and is a constant. Logarithm solves another problem - the proportionality of volatility to the absolute value, but not the clustering effect and other memory effects. When a stock was worth 1 rub and the daily volatility was 5%, which was 5 kopecks. When it grew to 10 rubles, the same 5% vol was 50 kopecks in absolute increments.
Which is exactly what I did several years ago. It was confirmed by stationarity tests - normal statistical tests. If you believe that series x(n)-x(n-1) is non-stationary, then there is nothing wrong with it either.
ok :)
И пора, наверное, уже завязывать со "случайностями" на рынках и обсасыванием характеристик СЧ. Весь форум уже захламлен подобными непрактичными рассуждениями.
In order to know how to make money, you must first understand exactly how you can't make money, so that you don't waste time on it later. And don't jump to conclusions about the impracticality of this or that approach; if you don't know how, it doesn't mean that no one else does.
1) Чтобы знать как можно заработать, необходимо сперва точно уяснить как заработать нельзя, чтобы потом не терять на это время.
2) Ну и не стоит делать скорополительных выводов о непрактичности того или иного подхода, если ты не знаешь как, это не значит что никто не знает.
1) Have you got it? That's good!
2) I'm not jumping to any hasty conclusions. Earn as much as you can and as well as you can, I have nothing against it.
ну если читали, то многократно упоминалось, что волатильность имеет память - зависимость от предыдущих значений. Стационарность же подразумевает, что дисперсия не зависит от предыдущих значений и является константой
Logarithm solves another problem - the proportionality of volatility to the absolute value, but not the clustering effect and other memory effects. When a stock was worth 1 rouble and the daily volatility was 5%, it was 5 kopecks. When the share grew to 10 rubles, the same 5% vol was 50 kopecks.
Don't get me wrong, there is no clear and precise definition of "time series memory". No one has, and making such fundamental discoveries should be done with extreme caution. Especially you write about stocks, while I write about the process x(n)-x(n-1). This process has nothing to do with stocks. It is a standard procedure for reducing series to a stationary one and is practically ironclad; it kills all or nearly all. But the series x(n)=x(n-1)+(case) is of course non-stationary, and everything you wrote directly applies to it.
Get it right, there is no clear and precise definition of "time series memory". No one has, and such fundamental discoveries should be made with extreme caution.
It has been written before, there is a model where volatility memory is taken into account.
Engle, Robert (b. 1942), American economist, specialist in methods for analyzing economic statistics. He was awarded the Nobel Memorial Prize in Economics in 2003 for his joint effort with Clive Grainger in analyzing time series with time-varying volatility.
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Although real volatility is variable, economists have for a long time had at their disposal only such statistical methods that are based on the assumption of its constancy. In 1982 Engle has developed the Autoregressive Conditional Heteroskedasticity (ARCH) model, on the basis of which changes in volatility can be predicted. His discovery of the method of economic time series analysis makes it possible to forecast the tendencies of GDP, consumer prices, interest rates, exchange rates and other economic indicators not only for the next day or week, but even for one year ahead with greater accuracy than before. The high accuracy of the forecasts made with the use of this model was proved, in particular, by analyzing the historical economic statistics of the USA and Great Britain when the forecasts based on the data of the previous years were compared with the actual indicators of the following years.
https://www.mql5.com/go?link=http://slovari.yandex.ru/dict/krugosvet/article/c/ca/1011225.htm
Писали же уже, есть модель где учитывается память по волатильности.
...No "time series memory" has ever been accounted for by this model. There is no need to be vaguely wishful thinking.
much more reliably than before, to predict trends in GDP, consumer prices, interest rates, exchange rates and other economic indicators not only for the next day or week, but even for a year ahead.
Have you ever tried forecasting using this method yourself?
No "time series memory" has ever been accounted for in this model. Don't be vaguely wishful thinking.
Have you ever tried forecasting using this method yourself?
Don't like the word memory, make it like Shiryaev's "aftermath". The model uses the dependence of volatility on previous values when forecasting. The fact that volatility and dispersion are not a constant but change with time and depend on previous values is simple and obvious. That's what is used in models like ARCH/GARCH. But you claim that the variance is constant. Although you may think so if you can find something useful from it :) The main value of models is to be practically useful.