Reconciling the Gaussian and Whittle Likelihood with an application to estimation in the frequency domain

Overview
Suppose ({Xt: t\in \mathbb{Z}}) is a second order stationary time series where (c® = \text{cov}(X{t+r},Xt)) and (f(\omega) = \sum{r\in\mathbb{Z}}c®e^{ir\omega}) are the corresponding autocovariance and spectral density fun…