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Say I have $n$ time series $y_1, y_2,...y_n$. Each $y_i$ being a vector of size $m$.

Given $y_i$ and $y_j$ the correlation $\rho(y_i,y_j)$ can be computed.

Say I want to scale the correlation up or down, that is change $\rho(y_i,y_j)$ to $\rho(y_i,y_j) + 10\% of \rho(y_i,y_j)$ (i.e change the current level of correlation to 10 percent more than what it is. ).

My question: Is there a way to achieve this by scaling the time series $y_i$ and $y_j$ ?

Meaning transform $f: y_i-> z_i$ for all i. such that

$\rho(z_i,z_j) = \rho(y_i,y_j) + 10\% of \rho(y_i,y_j)$

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  • $\begingroup$ what if $\rho(y_i,y_j)=0.95$ ? then you will have a hard time getting a correlation of $1.1$ since correlation is always between $-1$ and $1$... $\endgroup$
    – Surb
    Oct 12, 2019 at 20:08
  • $\begingroup$ that can be addressed by a bounding the correlation between 1 and -1 $\endgroup$ Oct 13, 2019 at 12:52

2 Answers 2

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A linear $f$ will not change the correlation.
A non-linear function might do that, but depends very much on the characteristics of the signals $y_i$.

Suppose for instance that the $y_i$ be quite similar for the lower values , while differing in the higher range. Then a compressing function (log for instance) would do the job.

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I think, This can be done by knowing the approximate function of dependent and independent variable by Taylor series or something like this then transform the data

Generally linear correlation not work well so try non linear regression (the above suggestion is based on this)

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