A note on the limiting spectral distribution of a symmetrized auto-cross covariance matrix

In Jin et al. (2014), the limiting spectral distribution (LSD) of a symmetrized auto-cross covariance matrix is derived using matrix manipulation. The goal of this note is to provide a new method to derive the LSD, which greatly simplifies the derivation in Jin et al. (2014). Moreover, as a by-product, the moment condition of the underlying random variables can be weakened from 2+δ2+δ to 22.