Debiasing Welch's Method for Spectral Density Estimation

Welch’s method provides an estimator of the power spectral density of a time series that is statistically consistent. This is achieved by averaging over periodograms calculated from overlapping segments of a time series. For a finite-length time series, while the variance of the estimator decreases as the number of segments increases, the magnitude of the estimator’s bias increases: a bias-variance trade-off ensues when setting the segment number.
We address this issue by providing a novel method for debiasing Welch’s method that maintains the computational complexity and asymptotic consistency, and leads to improved finite-sample performance. Theoretical results are given for fourth-order stationary processes with finite fourth-order moments and an absolutely convergent fourth-order cumulant function. The significant bias reduction is demonstrated with numerical simulation and an application to real-world data. For those less familiar with spectral analysis and the frequency domain I will start with a more gentle introduction to make the talk accessible.
The paper accompanying the talk is available in Biometrika under the same title. In collaboration with Lachlan Astfalck and Ed Cripps (University of Western Australia).