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Expert: - 12/18/2008


Question
Hi Scott

My major is Coastal Engg. I want to use TimeSeries calculations to translate some of my observations particularly 3D velocity components (u,v,w) in a river.
If it`s possible could you simply describe for me what does the cross-correlation of u and v represent?
Why Partial Cross Correlation is different with above?
Finally, explain me Cross-Spectrum of (u,v).
Actually, I can calculate all those, but I cannot understand what is the meaning of them!

Thanks  

Answer
The correlation between u and v is how much these two variables are dependent on each other.  If the correlation coefficient is 0, there is no correlation between the two variables.  If the correlation coefficient is 1, there is a perfect correlation between the two.  This means that if you know one value, you know the other value as well.

I believe the correlation coefficient is rx*ry/r²xy where rx is the rho value calculated with respect to x, ry is the rho value calculated with respect to y, and r²xy is the square of the rho value calculated between x and y, but you probably knew that already.

I have never seen partial cross corelayion between two variables.

If I knew exactly how to compue them, I would be able to give a better understanding to what them meant.

I found one paper in which I found what follows.  It was
http://ccrma-www.stanford.edu/~jos/log/Cross_Correlation.html
.
The DFT of the cross-correlation may be called the cross-spectral density, or `cross-power spectrum,' or even simply `cross-spectrum'.
This is somehow used on the correlation between two variables.

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Scott A Wilson

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I can answer any question in general math, arithetic, discret math, algebra, box problems, geometry, filling a tank with water, trigonometry, pre-calculus, linear algebra, complex mathematics, probability, statistics, and most of anything else that relates to math. I can even tell you it takes me over 2,000 steps to go a mile, but is that relevant?

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My master's paper was published in the OSU journal. The subject of it was Numerical Analysis used in shock waves and rarefaction fans. It dealt with discontinuities that arose over time. They were solved using the Leap Frog method. That method was used and improvements of it were shown. The improvements were by Enquist-Osher, Godunov, and Lax-Wendroff.

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Master of Science at OSU with high honors in mathematics. Bachelor of Science at OSU with high honors in mathematical sciences. This degree involved mathematics, statistics, and computer science. I also took sophmore level physics and chemistry while I was attending college. On the side I took raquetball, but that's still not relevant.

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I earned high honors in both my BS degree and MS degree from Oregon State. I was in near the top in most of my classes. In several classes in mathematics, I was first. In a class of over 100 students, I was always one of the first ones to complete the test. I graduated with well over 50 credits in upper division mathematics.

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