Pulsar timing arrays have recently provided strong evidence for a nanohertz stochastic gravitational wave background, motivating searches for deterministic gravitational wave signals from localized sources. Most existing searches assume specific waveform templates, which can be potentially insensitive to unexpected signals. We introduce a waveform-agnostic framework that models signal-induced timing residuals via a Fourier expansion. A Lorentzian profile is imposed on the variances of the Fourier coefficients, providing a flexible spectral envelope that captures the signal’s dominant frequency and bandwidth while remaining agnostic to its exact shape. Analytical marginalization over the Fourier coefficients then yields a Bayesian hierarchical framework that concurrently infers the source sky location, its frequency content, and the stochastic background. To mitigate contamination from unmodeled pulsar noise, we also include a pulsar-specific excess process with a frequency-independent power spectrum for the timing residuals. Tests on simulated datasets show that the method is robust and provides a flexible tool for future pulsar timing array searches, with sensitivity to both expected and unexpected gravitational wave phenomena.

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• Gravitational wave detection
• Gravitational wave sources
• Gravitational waves
• Neutron stars & pulsars
• Data analysis