Re: some basic questions on time series analysis
- From: "Dr Frederik R. Martin" <fr.martin@xxxxxxxxx>
- Date: Wed, 27 Apr 2005 16:27:23 +0200
May be you'll can find some answers about time series analysis at
http://www.euroestech.com
"Roger Bagula" <rlbagulatftn@xxxxxxxxx> a écrit dans le message de news:
426E5D87.1060500@xxxxxxxxxxxx
> The problem you seem to be talking about is related to sand piles
> and their application to earthquake theory.
> Per Bak's classic book :
> http://www.amazon.com/exec/obidos/tg/detail/-/0387947914/qid=1114528945/sr=1-1/ref=sr_1_1/104-6211140-5094309?v=glance&s=books
>> Editorial Reviews
>> Reason, Steven Postrel
>> . . . In print, at least, what might seem arrogant comes across as a kind
>> of innocent, childlike enthusiasm, a lack of concern
>>for anything but the sheer joy of figuring things out. His ruthless
>>simplifications of geology, evolution, and neurology pay off
>>because, as Bak notes, his models describe behavior that is common across
>>these domains. This universality means that trampling across others' turf
>>is not only acceptable, but almost mandatory,
>>if the underlying principles are to be exposed. Finally, for the most
>>part, Bak wants the reader
>>to grasp the basic logic of his arguments; only rarely does he try to
>>persuade with flights of poetic language or brute intellectual authority.
>
> paul wrote:
>
>> Hi,
>>
>> Based on physical understanding of the stress-strain relationship for
>> soils, some persons feel that there exists an attractor for the
>> stress-strain curve. I just came across time series analysis and it
>> struck me that if there does exist an attractor, then the methods of
>> time-series analysis should indicate whether this is the case or not.
>>
>> So, I did a bit of reading and applied the basic methods to the data
>> that I have available. I have requested more advanced books from the
>> local library, but in the meantime, have the following basic questions,
>> that I thought I would ask this group.
>>
>> 1. Can the time series analysis methods be applied to stress-strain
>> data. I have readings of stress vs. strain taken at uniform strain
>> increments. The test is run at a constant strain rate. I think the
>> answer to my question is yes, just want to confirm.
>>
>> 2. As the test proceeds, the soil sample deforms, bringing in a strain
>> (time) dependant error, and so, I assume, making time a relelvant
>> variable i.e. the coupled non-linear system of equations that describe
>> this test are probably non-autonomous. Question: does this impact my
>> Time Series Analysis in any different way?
>>
>> 3.I have data for six tests. For each test, I have a time series
>> analysis for the hydrostatic stress and the octahedral stress q. I
>> treat each independantly as a time series and find that the dimension
>> of the attractor saturates at a value between 0.9 and 1.1. From my
>> reading I know that a 1D attractor implies a line. What does an
>> attractor that is a non-integer whose value is close to one mean?
>>
>> 4. My phase space portraits typically can be approximated as two
>> straight lines, connected by a curve, the first line at an angle of say
>> 70 degrees to the horizontal and the second at say 30 degrees to the
>> horizontal, and heading out at this angle, as a straight line. What
>> does this mean if anything?
>>
>> 5. The embedded dimension seems to be between 1 and 5 depending on how
>> one defines saturation at the resulting curve. So typically, I get the
>> following points on the graph of Correlation Dimension vs. Embedded
>> Dimension (0.94,1) (1.01, 2) (1.04, 3) (1.07, 4) (1.1, 5) (1.1, 6)
>> (1.1, 7) From other theory, it should be two (if time is not a
>> variable) and three if time is a varaible. When is saturation reached
>> for data such as the one shown above?
>>
>> 6. Related to the question above, I suppose that the embedded
>> dimension, being that it deals with the number of relevant variables,
>> has to be an integer? Given that the sample deforms with time and that
>> this may be bringing in "error" and impacting the values, is time one
>> of these dimensions?
>>
>> 7. Also, from the data, I get that the first AMI minimum is found at a
>> time lag of between 5 to 19, and usually is around 7. I use this value
>> of the time lag to get the embedded dimension and correlated dimension.
>> My question is, what is the physical significance of the time lag? My
>> results (fortuneately) don't seem to be too sensitive to the actual
>> value chosen.
>>
>> 8. I have also come across a number of papers with titles such as "Does
>> the Length of Day have a Strange Attractor" and "Strange Attractor of
>> the Geomagnetic Field Variation" etc. Usually they calculate the
>> Correlation Dimension and the Embedded Dimension and show some phase
>> portaits. My question is this: In a classic paper of this type, what
>> needs to be shown in addition to these to prove that there is a
>> Attractor (strange or otherwise) in the physical process being
>> observed.
>>
>> Thank you very much!
>> Paul
>>
>
>
> --
> Roger L. Bagula email: rlbagula@xxxxxxxxxxxxx or
> rlbagulatftn@xxxxxxxxx
> 11759 Waterhill Road,
> Lakeside, Ca. 92040 telephone: 619-561-0814}
.
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