A New Spectral Density Decomposition for CARMA Models with Applications to Astronomical Data

3105 

Contributed Abstract 

Poster 

Darlin Soto (1), Giovanni Motta (2), Malgorzata Sobolewska (3), Francisco Cuevas (4)

(1) Universidad del Bío Bío, N/A, (2) Columbia University, N/A, (3) N/A, N/A, (4) universidad técnica federico santa maría, N/A

Giovanni Motta  
Columbia University

Malgorzata Sobolewska  
N/A

Francisco Cuevas  
universidad técnica federico santa maría

Darlin Soto  
Universidad del Bío Bío

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.

Spectral Density|CARMA models|Astronomical time series|Quasi-periodic oscillations|State-space models|

Astrostatistics Interest Group

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