  Extracting the spectral representations of the neural processes that underlie
spiking activity is key to understanding how the brain rhythms mediate
cognitive functions. While spectral estimation of continuous time-series is
well studied, inferring the spectral representation of latent non-stationary
processes based on spiking observations is a challenging problem. In this
paper, we address this issue by developing a multitaper spectral estimation
methodology that can be directly applied to multivariate spiking observations
in order to extract the evolutionary spectral density of the latent
non-stationary processes that drive spiking activity, based on point process
theory. We establish theoretical bounds on the bias-variance trade-off of the
proposed estimator. Finally, we compare the performance of our proposed
technique with existing methods using simulation studies and application to
real data, which reveal significant gains in terms of the bias-variance
trade-off.
