Quasi-Periodic Gaussian Process Modeling of Pseudo-Periodic Signals

Pseudo-periodic signals are frequently encountered in modern scientific and engineering applications. Most current signal modeling methods focus on strictly periodic signals, and they may fail to account for both the within- and between-period correlations of pseudo-periodic signals, which could lower the modeling and prediction accuracy. To address this issue, we develop a novel quasi-periodic Gaussian process method for signals collected at grids. It can well model the within- and between-period correlations and has an easy-to-interpret structure that can quantify the magnitude of cycle oscillations in pseudo-periodic signals. To speed up the model estimation, prediction, and simulation, we further propose a fast composite likelihood approach that decomposes the full likelihood in an exact manner. This acceleration is achieved by leveraging the fast Fourier transform (FFT) and exploiting the Kronecker structure of the within- and between-period correlations. Its superior performance over some state-of-the-art methods is demonstrated through a simulation study and two real case studies on sunspot period estimation and cardiac arrhythmia monitoring.