Functional Spectral Analysis for Time Series Classification

：Kun Chen (Southwestern University of Finance Economics)
： 2026-03-12 16:30
：Conference Room C503 at Administration Building at Haiyun Campus

Speaker：Kun Chen (Southwestern University of Finance and Economics)

Time：2026-3-12 16:30

Location：Conference Room C503 at Administration Building at Haiyun Campus

Abstract:

Traditional spectral classification methods for stationary time series typically characterize differences based on vectors of periodogram ordinates, or their logarithms, evaluated at discrete frequencies. However, these estimators often fail to leverage the intrinsic smoothness of the underlying (log-)spectral density function. This paper proposes a novel Spectral Functional Classification (SFC) procedure that addresses this limitation by treating the smoothed log-periodogram as a functional object. Specifically, by employing Functional Principal Component Analysis, the procedure extracts the most important components of the spectral density and achieves a significant denoising effect by filtering out stochastic noise. We further introduce a data-driven procedure for selecting the optimal number of principal components. Under mild conditions, we establish the consistency of our estimators and provide a rigorous proof of classification consistency, demonstrating that the misclassification probability vanishes in the double-asymptotic regime (as both the number of time series n and the series length T approach infinity). Extensive simulations and a real data application demonstrate the superior accuracy and robustness of the SFC approach compared to existing methods.