Suppose I have two time-series variables, $\{x_t\}$ and $\{y_t\}$, where $t\in[1,T]$. I would like to model the correlation $\rho(x_t,y_s)$ as some function of $t$,$s$, and the difference $t-s$. In other words, $\rho_{t,s}$ may take on a different value for any valid combination of $(t,s)$, a total of $\frac {T(T+1)}2$ correlations, but I would like to economize on the number of estimated correlations (as well as possibly improving the output) by applying some sort of model.

In the actual application I have in mind, these are macroeconomic and/or financial variables. The derived correlations are used to derive a full pseudo-correlation matrix, which is transformed into the nearest true P.S.D. correlation matrix using Higham's (2002) algorithm.

  • 1
    $\begingroup$ Can you give an idea of the size of the dataset (i.e. T=?,S=?)? Is there a reason why you don't model the time varying correlation matrix directly (DCC garch)? $\endgroup$
    – user603
    Jul 26, 2011 at 21:18
  • $\begingroup$ @user603 T is the same for both x and y, and it is about 600. Furthermore, there are about 30 such variables, and I need pairwise correlation between each of them. I am not familiar with DCC GARCH, I will look into it. However, the idea here is to find a correlation between $x$ at time $t$ and $y$ at time $s$ (not both at $t$). $\endgroup$ Jul 27, 2011 at 15:06
  • $\begingroup$ 30 is a bit larger than what i had in mind and probably too large for DCC to work (tough numerical rountines may have improved, check the package rgarch.r-forge.r-project.org). Indeed, a matrix reconstrution approach as in Higham's may be best here. $\endgroup$
    – user603
    Jul 27, 2011 at 16:00
  • $\begingroup$ I don't think DCC is what you want since it looks like you're asking for constant correlation coefficients? $\big($By the fact that you didn't specify $\rho(x_t,y_s)(t)$, $\rho(x_t,y_s)_t$ or $\rho_t(x_t,y_s)$ $\big)$. $\endgroup$
    – Jase
    Dec 8, 2012 at 15:11

1 Answer 1


It may be a little bit late for you, but for future readers. I think what you are looking for is some sort of cross-correlation.


  • $\begingroup$ This is being automatically flagged as low quality, probably because it is so short. At present it is more of a comment than an answer by our standards. Can you expand on it? We can also turn it into a comment. $\endgroup$ May 29, 2017 at 12:22

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.