Can I use PartialCorrelationFunction on multivariate data?

I am doing a bit of work on multivariate time series and I need to calculate the partial autocorrelation function of a matrix. I will provide some details bellow and show an example of how I simulate my data:

Data simulation First I create an autoregressive process that I need for my work. Mathematica’s ARProcess does not seem to work on multivariate data directly, however, I managed to find a workaround for that:

aCoef = {{{0, 0, 0, 0}, {0, 0, 0, 0.8}, {0, 0, 0, 0}, {0, 0, 0.8, 0}}, {{0, 0, 0, 0}, {0.8, 0, 0, 0},{0, 0, 0, 0}, {0.8, 0, 0, 0}}};

These coefficients allow me to simulate data that have 4 paths in the time series that influence each other in different time lags. Now that my coefficients are defined, I am simulating the data like this:

data = RandomFunction[ARProcess[aCoef, IdentityMatrix[4]], {0, 10000}];

Now what this process does, is to create a TemporalData object, which can be used for my further analysis. I would like to see what the partial autocorrelation is between the different channels. This will allow me to see if the simulated data are as I expect. I would expect to be able to use a function that would output something like this:

A matrix of the output of pacf function from R

This is the output of the pacf function in R, that I have implemented using REvaluate in Mathematica. It shows that there are values different from zero, where expected, i.e. the fourth element of the matrix on row 1, column 2, the third element of the matrix on row 1 column 4, the first element of the matrix on row 2 column 2 and finally the first element of matrix on row 2 column 4. The matrix rows represent time lags and the columns represent each path of the time series. I have tried using PartialCorrelationFunction: Output of the fucntion

According to the Wolfram Documentation, either data or tproc can used as 1st argument in that function, I have tried both with no success. Although this is not an error in the language, it does not provide the information I am looking for. I could use the R function, but ideally I would like to use the functions in Wolfram. Does anyone have any idea on how to fix this? Thanks!