A Dynamical Equation Approach For Quasi-Periodic Gaussian Processes

Quasi (pseudo/approximate) periodic signals often occur in natural settings, particularly when a periodic signal is recorded with noise. In this work, we develop a new dynamical equation system to construct a family of Quasi-periodic Gaussian Processes (QPGP). We provide a computationally inexpensive algorithm based on a newly derived likelihood function for parameter estimation. Our approach also simplifies the signal forecasting. We illustrate via a simulation study that the proposed QPGP estimation strategy is faster as well and more accurate than existing constructions. Unlike these existing models, the proposed approach extends to multiple families of kernels, which we illustrate by modeling sunspot data with both periodic Matérn and MacKay's covariance kernel. This shows the exclusive advantage of the new QPGP family proposed in this work.