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What can one conclude if the distributions are close enough by the chi^2 measure? In particular can we infer something about the veracity of using TA? Frankly, I think the answer is no, at least not always. The distribution and chi^2 does not say anything about the time behavior of a process (should be obvious since the data is treated as a collection, not as a series!).
Consider the following degenerate, contrived, hypothetical data. (Notice there is a use for synthetic data... ) The attached image has two curves - one is a normal distributed random sequence, the next is the same set of numbers sorted in ascending order. The numbers are exactly the same, chi-squared is 0 and, hence, both derive from the statistically same set of randomnumbers.
Clearly, both curves are not a "random walk process". The monotonically increasing sort is clearly dependant on history, the next number is always selected to be greater than all preceding. If I can find a stock with that behavior I'm home free - any thoughts Steve <g>.
Anyway, this helped to clarify my thoughts. Perhaps you will also find it stimulating.
Cheers,
Richard
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<DIV><FONT face=Arial size=2>I have been thinking about the meaning of
chi-squared tests (and others). As I understand chi^2, it compares
distributions, basically looking at a variance of the test vs. the sample
distribution histograms.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>What can one conclude if the distributionsare
close enough by the chi^2 measure? In particular can we infer something
about the veracity of using TA? Frankly, I think the answer is no, at
least not always. The distribution and chi^2 does not say anything
about the time behavior of a process (should be obvious since the data is
treated as a collection, not as a series!).</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>Consider the following degenerate, contrived,
hypothetical data. (Notice there is a use for synthetic data... )
The attached image has two curves - one is a normal distributed random sequence,
the next is the same set of numbers sorted in ascending order. The numbers
are exactly the same, chi-squared is 0 and, hence, both derive from the
statistically same set of random numbers.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>Clearly, both curves are not a "random walk
process". The monotonically increasing sort is clearly dependant on
history, the next number is always selected to be greater than all
preceding. If I can find a stock with that behavior I'm home free - any
thoughts Steve <g>.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>Anyway, this helped to clarify my thoughts.
Perhaps you will also find it stimulating.</FONT></DIV><FONT face=Arial size=2>
<DIV><BR>Cheers,</DIV>
<DIV> </DIV>
<DIV>Richard</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
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align=baseline border=0></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
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