2024/10/03 by Yuping Zheng, Zheng, Yuping, Andrew Lamperski +1 · 1 citation
Decision Sciences · Economics, Econometrics and Finance · Engineering · #Advanced Statistical Process Monitoring #Complex Systems and Time Series Analysis #FOS: Mathematics #Fault Detection and Control Systems #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2410.02951
openalex publication_date 2024/10/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Spectral estimation is a fundamental problem for time series analysis, which is widely applied in economics, speech analysis, seismology, and control systems. The asymptotic convergence theory for classical, non-parametric estimators, is well-understood, but the non-asymptotic theory is still rather limited. Our recent work gave the first non-asymptotic error bounds on the well-known Bartlett and Welch methods, but under restrictive assumptions. In this paper, we derive non-asymptotic error bounds for a class of non-parametric spectral estimators, which includes the classical Bartlett and Welch methods, under the assumption that the data is an L-mixing stochastic process. A broad range of processes arising in time-series analysis, such as autoregressive processes and measurements of geometrically ergodic Markov chains, can be shown to be L-mixing. In particular, L-mixing processes can model a variety of nonlinear phenomena which do not satisfy the assumptions of our prior work. Our new error bounds for L-mixing processes match the error bounds in the restrictive settings from prior work up to logarithmic factors.