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Accurate forecasting of the UK gross value added (GVA) is fundamental for measuring the growth of the UK economy. A common nonstationarity in GVA data, such as the ABML series, is its increase in variance over time due to inflation. Transformed or inflation-adjusted series can still be challenging for classical stationarity-assuming forecasters. We adopt a different approach that works directly with the GVA series by advancing recent forecasting methods for locally stationary time series. Our approach results in more accurate and reliable forecasts, and continues to work well even when the ABML series becomes highly variable during the COVID pandemic. [ABSTRACT FROM AUTHOR]

Spectral estimation is a fundamental task in signal processing. Recent algorithms in quantum phase estimation are concerned with the large noise, large frequency regime of the spectral estimation problem. The recent work in Ding-Epperly-Lin-Zhang proves that the ESPRIT algorithm exhibits superconvergence behavior for the spike locations in terms of the maximum frequency. This note provides a perturbative analysis to understand this behavior and extends to the case where the noise grows with the sampling frequency. However, this does not imply or explain the rigorous error bound obtained by Ding-Epperly-Lin-Zhang. [ABSTRACT FROM AUTHOR]