Hearst index - page 37

New comment
 

Why go so far?

I'd rather deal with ordinary turkeys...

 
faa1947:

I always try to find the optimum window width in my TCs. It varies between 30-70 observations (for H1).


What kind of window exactly? For example, a Gaussian one suppresses boundary effects very significantly compared to a regular rectangular one (it will also be Gaussian in the frequency domain, i.e. it will give -40 dB per octave without any side maxima). The same reactivity can then be achieved by taking more signal values into account.
 
Dersu:

Why go so far?

I'd rather deal with ordinary turkeys...


Who's that?)
 
Private Dersu !
 
Dersu:
Private Dersu !

At ease! What are these envelopes, red and green?
 

Envelopes as envelopes.

Inserted.

 
A celebration?
 

Saturday, holiday...

Get off the subject ?

 
faa1947:

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:

Some time series exhibit marked correlations at high lags, and they are referred
to as long-memory processes. Long-memory is a feature of many geophysical
time series. Flows in the Nile River have correlations at high lags,
and Hurst (1951) demonstrated that this affected the optimal design capacity
of a dam. Mudelsee (2007) shows that long-memory is a hydrological property
that can lead to prolonged drought or temporal clustering of extreme
floods. At a rather different scale, Leland et al. (1993) found that Ethernet
local area network (LAN) traffic appears to be a statistically self-similar and a
long-memory process. They showed that the nature of congestion produced by
self-similar traffic differs drastically from that predicted by the traffic models
used at that time. Mandelbrot and co-workers investigated the relationship
between self-similarity and long term memory and played a leading role in

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. At any rate, 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 we should first find cotiers. in which long memory?

You can identify this long memory in any quotes. But ACF is not suitable here.
Peters gives an interesting definition of long memory. Read it. There is a lot of interesting information in his books on this subject. According to him such processes cannot be measured by trivial ACF. ACF works on a scale of 5-6 lags and that's it. If H is expressed as a moving particle with spread equal to square root of distance, then we get a special case of normal distribution StdDev = Sqrt(T) = T^(0.5). Now, if the scattering of the particle is slightly above or below 0.5 it is possible in one and only one case: the particle must remember its past state and hence such a process will possess a memory. I.e. H is not a characteristic of external action, but depends on previous state of the process. And if the escape trajectory is preserved, it means that it depends on previous values and the memory period can be calculated. And it often happens that on all scales of calculations the slope angle does not change, and at the same time, it is not equal to 0.5. In this case, the process is said to be a true Hearst process with infinite memory. Except that ACF will not show anything of the kind.
 
C-4:
You can identify this very long memory in any quotes. But ACF is not suitable here.
Peters gives an interesting definition of long memory. Read it. There is a lot of interesting stuff in his books on this subject. According to him such processes cannot be measured by trivial ACF. ACF works on a scale of 5-6 lags and that's it. If H is expressed as a moving particle with spread equal to square root of distance, then we get a special case of normal distribution StdDev = Sqrt(T) = T^(0.5). So, if the scattering of the particle is slightly above or below 0.5 it is possible in one and only one case: the particle must remember its past state and hence such process will possess a memory. I.e. H is not a characteristic of external action, but depends on previous state of the process. And if the escape trajectory is preserved, it means that it depends on previous values and the memory period can be calculated. And it often happens that on all scales of calculations the slope angle does not change, and at the same time, it is not equal to 0.5. In this case, the process is said to be a true Hearst process with infinite memory. Except that ACF will not show anything of the kind.

Unfortunately, I do not have my own opinion on this matter.

But I can refer you to the book

Cowpertwait and A.V. Metcalfe, Introductory Time Series with R, 159

Use R, DOI 10.1007/978-0-387-88698-5 8,

© Springer Science+Business Media, LLC 2009

Chapter 8 of which describes the FARIMA fitting process. ACF is used in this process.

Attached is the text. Unfortunately, the formulas and theoretical part did not turn out.

But the FARIMA fitting process is specifically described

Files:
long.zip  203 kb
1...303132333435363738394041424344...46
New comment