Does anyone know if there’s a native Julia implementation of finding the Nearest Correlation Matrix?
I am not aware of any.
Essentially you have to solve a semidefinite program, which can be done using e.g. JuMP and an appropriate SDP solver.
I created a simple example as a test case for my solver here:
https://github.com/oxfordcontrol/COSMO.jl/blob/master/examples/closest_correlation_matrix.jl