Contributed Poster Presentations: Astrostatistics Interest Group

Modeling the power spectral density (PSD) of astronomical time series is key to characterizing variability and identifying quasi-periodic oscillations (QPOs) in X-ray binaries. Standard approaches rely on periodogram-based methods and Lorentzian fitting, which separate estimation from modeling and may limit interpretability. We propose a new spectral density decomposition for continuous time autoregressive moving-average (CARMA) models that provides a direct and interpretable representation of the PSD. The decomposition expresses the CARMA spectral density as a finite sum of component functions determined by the real and complex roots of the autoregressive polynomial, with each component associated with a distinct spectral feature. Estimation is performed using the state-space representation of CARMA models under both classical and Bayesian frameworks. We apply the method to X-ray light curves from the Rossi X-ray Timing Explorer, showing that it captures broadband variability and quasi-periodic behavior and allows us to assess whether the observed variability is better explained by one or multiple dominant spectral peaks.