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  The roots of the auto-regressive polynomial, $\rho_{p}$, indicate timescales on which variability presents itself. The auto-correlation function of a CARMA(p,q) process goes as    $$R(\tau) = \sigma^2\sum_{k=1}^{p}\frac{e^{\rho_{k}\tau}\big[\sum_{l=0}^{q}\beta_{l}(-\rho_{k})^{l}\big]\big[\sum_{l=0}^{q}\beta_{l}\rho_{k}^{l}\big]}{-2Re(\rho_{k})\prod_{l=1,l\ne k}^{p}(\rho_{l}-\rho_{k})(\rho_{l}^{*}+\rho_{k})}  $$ $$ where $Re(\cdot)$ is the real part and $z^{*}$ is the complex conjugate of $z$. The roots here are assumed to be unique as a consequence of the operation of the Kalman filter which will be discussed later.    *then the PSD