Math Question

Ok I know there are some math gurus on ET ....

I have two time series, Series A and Series B. Series B is somewhat correlated to Series A. I want to find the signal from Series B less any influence from Series A. I already normalized each series - I detrended (I don't care about difference in overall trend) and divided by the standard deviation.

(Series A) - (Series B * bMult) = Series C

I figure if A and B are highly correlated, bMult should be nearly 1. If they are not very correlated, bMult should be nearly 0. Maybe I am looking for the bMult that minimizes the std. dev. of Series C.

 

what do you mean find the "signal". maybe just do a regression

 

You have two time series that are correlated. Fine. Then you detrend. Again fine, but I have no idea why anyone would want to do that except for studying volatility.

What is the correlation after you detrend?

 

Rewrite as ordinary least squares regression:

A = bMult*B + C

where C is your vector of residuals

Solve for bMult:

bMult = (B'*B)^-1 * B' * A

where B' means B-transpose

This will minimize the sum of squares of C and, by
construction, its standard deviation.

 

To detrend each series, I subtracted the linear regression.

 

Regardless if it is strong or weak correlation, I want to break B into two components. One component follows A and the other component represents the "noise".

 

I think I understand this.

And I just realized ....

Series A is ALREADY subtracted from it's ordinary least squares regression and then divided by it's standard deviation.
Same with Series B.

So maybe I just need to take the difference (subtract) .... no multiplier needed. And this difference will already have a minimized standard deviation.

 

But then again, you need multiplier for B .... if A and B were the inverse of each other, a multiplier of -1 would be perfect. A - (B * -1) would equal zero giving a zero noise component .... perfect.

Sorry I am rambling ..... I am clinically insane. Kind of like the guy from Pi but not even that smart

 

I said signal because I think this is the kind of stuff they do in signal processing. I want to subtract signal A from signal B but I'm not sure how much of signal A exists in signal B. The inverse of signal A may even exist in signal B. In any case, I want see signal B with any influences from signal A subtracted out.