Hearst index - page 23
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I understand that not many people are interested in the topic at the moment. Perhaps we should wait another 5-10 years...
What an amazing thing is this "fractal statistics". Kind of Mandelbort first described this method in late 60's (45 years ago!), kind of in late 80's and mid 90's (20 years ago) his ideas were developed by Peters. It seems to have all the formulas and graphs. And how to correctly calculate these simple formulas, even mathematicians with their powerful Matcads and Matlab do not know. This is a paradox...
Apparently I will have to keep this thread on the front page artificially for some time. Maybe some knowledgeable person will be merciful and finally help me solve the problem...
I understand that not many people are interested in the topic at the moment. Perhaps we should wait another 5-10 years...
What an amazing thing is this "fractal statistics". Kind of Mandelbort first described this method in late 60's (45 years ago!), kind of in late 80's and mid 90's (20 years ago) Peters developed his ideas. It seems to have all the formulas and graphs. And how to correctly calculate these simple formulas, even mathematicians with their powerful Matcads and Matlab do not know. This is a paradox...
Apparently I will have to keep this thread on the front page artificially for some time. Maybe some knowledgeable person will show mercy and finally help me solve the problem...
I was able to do a proper calculation of the Hearst index in Excel, somewhere the file is lying around. But I'll be honest with you, I don't see how to apply it without additional concepts in trading. The usual approach: if the Hurst value for some period is larger than 0.5 - wait for trend continuation, if it is less, wait for pullback movements. Everything is extremely vague...
For simplicity, you can trivially calculate covariance on a period and the result will be really similar to Hearst.
I was able to do a proper calculation of the Hearst figure in Excel, I have a file somewhere. But frankly speaking, I don't see how to use it without additional concepts in trading. Usually they advertise the following approach: if Hearst is more than 0.5 for a certain period - wait for trend continuation, if it is less - wait for pullback movements. Everything is extremely vague...
For simplicity, you can trivially calculate covariance on a period and the result will be really similar to Hearst.
I understand what you're saying, but it's all wrong. I know what I'm talking about, because I've read the primary source and I found the ideas in it interesting. The notion of what Hearst's statistics are has been greatly perverted by technical analysis. R/S analysis has been turned into a really useless oscillator a la RSI. But it's all about understanding. For example, take the same Moving Average- everyone knows that it is late by about the number of averaging periods divided by two. In fact, Moving Average is not late, it just shows average state of process for the chosen period. The reason why it can't be used, is that we are trying to look into the future based on this moving average. The Moving Average doesn't show the future like any other indicator, it simply tells us about the process characteristics. But we can make right decisions in the present based on knowledge of the past characteristics, which in turn will lead to positive results in the future. Different statistics whether it's R/S analysis or Moving Average allows us to collect typical process maps that can be of interest to us.
I understand that not many people are interested in the topic at the moment. Perhaps we should wait another 5-10 years...
What an amazing thing is this "fractal statistics". Kind of Mandelbort first described this method in late 60's (45 years ago!), kind of in late 80's and mid 90's (20 years ago) his ideas were developed by Peters. It seems to have all the formulas and graphs. And how to correctly calculate these simple formulas, even mathematicians with their powerful Matcads and Matlab do not know. This is a paradox...
Apparently I will have to keep this thread on the front page artificially for some time. Maybe some knowledgeable person will be merciful and finally help me solve the problem...
An interesting manuscript, something to read. But so far I've run into the problem of the trivial repeatability of the results. Peters does the experiment, his result:
I do the experiment, on the same data, using the same formulas and methodology:
Obviously the result is different. The conclusion is that there's probably an error in the calculation. I need to understand what I am doing wrong and where the error is.
However, I tend to believe that I have an error, because the R/S range cannot become smaller with increasing period, or even wobble on the horizontal, and my last value is less than the previous ones. This cannot be even in theory, because even for antipersistent series the slope angle H should be less than 0.5, but never less than zero, which is visible in my case.
Now I'm busy partitioning calculations into pure C#, it's easier to work with data there. After I rewrite it into normal form, I'll start to analyze the situation.
o.k. Here is the CSV file of the S&P 500 from 01.01.1950 to 01.07.1988.
p.s. I could really use such help. I desperately need a benchmarking of the calculation from outside, only then can I talk about the reliability of the result.
I'll do my best. I'll try not to take too long.
I don't have Peters. I'm basing it on E. Feder. Fractals. M. Mir. 1991.