Bayesian nonparametric estimation of the spectral density of a long memory Gaussian time series

Judith Rousseau, Brunero Liseo

Let $\mathbf{X}=\{X_t,t=1,2,...\}$ be a stationary Gaussian random process, with mean $E{X}_t=\mu$ and covariance function $\gamma (\tau )=E(X_t-\mu )(X_{t+\tau }-\mu )$. Let $f(\lambda )$ be the correspondin…