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I am currently working with panel data, namely its correlations. The data is three-dimensional. I am looking for a way to aggregate the correlation coefficients. I found a model which uses the Fisher transformation to do this as shown as follows:

Let $i$ be an invidual (20), consisting of 5 buckets $b$, each containing its own time-series, $j$, $n_j = 3000$ For example, 20x3000x5.

$\rho_{i,j} = \frac{e^{2z}-1}{e^{2z}+1} $

$ z = \frac{1}{\sum_{ib}^{N}n_{i,b}} \sum_{ib}^{N}n_{ib}(\frac{1}{2} ln(\frac{1+\rho_{ib}}{1-\rho_{ib}})) $

Assume $i$ and $j$ follow bivariate normal and are i.i.d.

Why would this be a legitimate way of aggregating the correlation coefficients, if it is at all?

EDIT:

So there is a financial application actually, there are 20 assets i, each of them has a time-varying standard deviation j so time-series with 3000 observations, but the standard deviations are divided by so called maturity buckets b "up to 30days", "up to 60 days" etc. The n-dimensional array is 20 by 4 by 3000.

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  • $\begingroup$ Could you explain what "20x3000x5" means and how it might be related to "additional 4 buckets"? How do you intend to interpret the aggregated correlation coefficients? $\endgroup$
    – whuber ♦
    Commented Dec 5, 2019 at 16:17
  • $\begingroup$ So there is a financial application actually, there are 20 assets $i$, each of them has a time-varying standard deviation $j$ so time-series with 3000 observations, but the standard deviations are divided by so called maturity buckets $b$ "up to 30days", "up to 60 days" etc. The n-dimensional array is 20 by 4 by 3000. $\endgroup$
    – deblue
    Commented Dec 5, 2019 at 16:27

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