Optimally adaptive Bayesian spectral density estimation for stationary and nonstationary processes
This work provides an incremental improvement in spectral density estimation for time series analysis, primarily benefiting statisticians and researchers in fields like physical sciences.
The authors tackled the problem of estimating spectral density for stationary and nonstationary time series by optimizing an eigendecomposition with a smoothing spline covariance structure, resulting in material improvements over existing methods as validated through simulations and real data.
This article improves on existing methods to estimate the spectral density of stationary and nonstationary time series assuming a Gaussian process prior. By optimising an appropriate eigendecomposition using a smoothing spline covariance structure, our method more appropriately models data with both simple and complex periodic structure. We further justify the utility of this optimal eigendecomposition by investigating the performance of alternative covariance functions other than smoothing splines. We show that the optimal eigendecomposition provides a material improvement, while the other covariance functions under examination do not, all performing comparatively well as the smoothing spline. During our computational investigation, we introduce new validation metrics for the spectral density estimate, inspired from the physical sciences. We validate our models in an extensive simulation study and demonstrate superior performance with real data.