Optimally adaptive Bayesian spectral density estimation for stationary and nonstationary processes

Abstract

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.

New experiments and contributions since v2. Equal contribution

References in corpus (4)

• Collective correlations, dynamics, and behavioural inconsistencies of the cryptocurrency market over time
• Comparing the dynamics of COVID-19 infection and mortality in the United States, India, and Brazil
• Structural clustering of volatility regimes for dynamic trading strategies
• A new measure between sets of probability distributions with applications to erratic financial behavior