We define a numerical method that provides a non-parametric estimation of the
kernel shape in symmetric multivariate Hawkes processes. This method relies on
second order statistical properties of Hawkes processes that relate the
covariance matrix of the process to the kernel matrix. The square root of the
correlation function is computed using a minimal phase recovering method. We
illustrate our method on some examples and provide an empirical study of the
estimation errors. Within this framework, we analyze high frequency financial
price data modeled as 1D or 2D Hawkes processes.