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To capture the slowly time-varying spectral content of real-worldtime-series, a common paradigm is to partition the data into approximatelystationary intervals and perform inference in the time-frequency domain.However, this approach lacks a corresponding nonstationary time-domaingenerative model for the entire data and thus, time-domain inference occurs ineach interval separately. This results in distortion/discontinuity aroundinterval boundaries and can consequently lead to erroneous inferences based onany quantities derived from the posterior, such as the phase. To address theseshortcomings, we propose the Piecewise Locally Stationary Oscillation (PLSO)model for decomposing time-series data with slowly time-varying spectra intoseveral oscillatory, piecewise-stationary processes. PLSO, as a nonstationarytime-domain generative model, enables inference on the entire time-serieswithout boundary effects and simultaneously provides a characterization of itstime-varying spectral properties. We also propose a novel two-stage inferencealgorithm that combines Kalman theory and an accelerated proximal gradientalgorithm. We demonstrate these points through experiments on simulated dataand real neural data from the rat and the human brain.

PLSO: A generative framework for decomposing nonstationary time-series into piecewise stationary oscillatory components