Hearst index - page 36
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I read mostly dissertations on the subject. And the calculation is taken from http://capital-times.com.ua/index.php?option=com_content&task=view&id=11623&Itemid=88888963
A very interesting topic. I would hope to get to know the result in the future.
As a contribution to the development of the topic.
FARIMA fractional-integrated models are used to apply the Hearst index. For these models there is a ready-made code for parameter estimation. Excel is not the right package to discuss. Unfortunately, the algorithms are implemented in R, a very bastard programming system. Maybe they are implemented somewhere else. Look for FARIMA and long run memory. In the attachment I've attached instructions from R on how to use FARIMA models. You can find plenty of literature here for very low cost. Search by time series and R. Lots of very good books.
Good luck. I hope you'll post the result on the forum, or at least in person.
The zero in the file in column D does not work because of errors in the formulas. The first one is in cell D87, and there are a dozen more in the text. Reblock this column, the rest seems to be correct (although check the RMS calculation as well).
About the rest. The Hurst coefficient is generally speaking an integral characteristic, i.e. it characterizes the random variable during the whole measurement period, rather than a point in its realization series. Therefore, in practice, we cannot say "we have calculated H", the correct way would be "we have estimated H". This is not snobbism, what I mean is that you will never know exactly what the Hearst value of a quantity was, as this information is only available to God, but you can only estimate its value with a certain degree of certainty, and the more observations you have, the more accurate the estimate will be. Hence, the answer to your question: to break the series into periods or not depends on whether you want to estimate the H exponent for the whole series or for some of its parts (nobody told us that it is constant in time, right?). You can simply take as N the number of observations in your sample.
I read mostly dissertations on the subject. And the calculation is http://capital-times.com.ua/index.php?option=com_content&task=view&id=11623&Itemid=88888963
This paper by Eric Nyman (2010), which in turn was written from a book by Adgar Peters (1990), who took this method from Mandelbort's works (1960-70), which first described a method invented by an old man Harold Edwin Hirst, 70 years old, in far 1951, for mass audience. It all means that when asked about novelty of proposed theme at dissertation advice, you should imagine that old Edwin from XIX century is an innovator of fractal geometry:)
But seriously, the method was developed, as seen above, to a specific and highly abnormal process - the Nile spill. In the picture below, the disproportionality of the spill spread to the overall trend or mathematical expectation is obvious. And so for a specific process - the Nile spill - this method is good and works, but for financial markets as Mandelbort has tried to present it, it is no longer sufficient. Under any circumstance and in any market, including SB, your calculation will show a value of about 0.54. You need other, more accurate methods. And as soon as you write a dissertation, you can not do without fractional integrated autoregressive moving average FARIMA, and it is only available in specialized statistical packages. H can be set arbitrary there. But this does not solve the problem, because in order to at least fit the market to the model, you need to calculate its H, and how can you do it if the most simple and common method does not work? There are other works on this theme, works by Pastukhov and Shiryaev. Look at them. They are more scientific and better suited for a dissertation, but whether they are more accurate is a question. There is also a related thread on the same topic, look here.
Well, not nineteenth century, but twentieth.
Oh, bullshit this Hearst really. Exactly alsu says it's something integral.
Well, it's not XIX, it's XX.
Hearst is rubbish really. Exactly alsu says it's something integral.
It's more like this - H is more a characteristic of the external environment (its "viscosity", "elasticity", etc.) than of the system itself. If transferred to a specific market instrument, here H is a quantitative characteristic of the external (fundamental, as we used to say) background: the mobility of ideas, typical actions of respective central banks, "temperament" of traders, etc. (compare behavior of Euro and Yen, for example), while currency pairs themselves in terms of internal model do not differ (the principles and rules of making transactions are the same for all instruments).
It's more like this - H is more a characteristic of the external environment (its "viscosity", "elasticity" etc) than of the system itself. If transferred to a specific market instrument, here H is a quantitative characteristic of the external (fundamental, as we used to say) background: the mobility of ideas, typical actions of respective central banks, "temperament" of traders, etc. (compare behavior of Euro and Yen, for example), while currency pairs themselves in terms of internal model do not differ (the principles and rules of making transactions are the same for all instruments).
If we look at " H is more characteristic of the external environment", we should pay attention to the English terms used in connection with Hirst. Here is a copy-paste from the BP monograph:
establishing fractal geometry as a subject of study.
Please note these words
Some time series exhibit marked correlations at high lags
И
shows that long-memory
I tried to find out: what is long-memory? It turns out autocorrelations over 40 observations! But in quotes such a long correlation of one sign is extremely rare. Anyway, after spending an hour, I didn't find it.
A large number of people try to use the Hurst index. Not once have I seen a positive result. Maybe you should find cotiers first. in which long memory?
A large number of people try to use the Hearst index. I have never seen a positive result. Maybe we need to find the quotients first. in which long memory?
Long memory means that H for a given value is significantly different from 0.5, which of course is not the case in quotients. The attempts to use it in this area fail mainly because H is very difficult to estimate reliably on a small sample, so the results on 100 and even 1000 candlesticks cannot be trusted. And at larger intervals H is rather close to a half, i.e. it gives rather small information (useful) about price behavior, at least such information that would allow to outplay the spread.
Long memory means that H for a given value is significantly different from 0.5, which of course is not the case in quotients. The attempts to use it in this area fail mainly because H is very difficult to estimate reliably on a small sample, therefore results on 100 and even 1000 candlesticks cannot be trusted. And at larger intervals H is rather close to a half, i.e. it gives rather small information (useful) about price behavior, at least such information that would allow to outplay the spread.
For me, the width of the window is quite important.
At a window width of a few hundred observations, the limit theorem starts to work, which gives an average temperature that starts moving very quickly towards its mo. And what is needed to predict, in fact, the next bar?
In my TCs I always try to find the optimal window width. It varies between 30-70 observations (for H1). After 118 (a week on H1) the picture changes sharply. That is why I have started to think about the term "long memory".
ZS. In the literature on fractionally integrated models, they usually write long memory, and in the introduction "Hurst, fractals, thick tails".