Discriminant Analysis in stationary time series based on robust cepstral coefficients

Abstract

Time series analysis is crucial in fields like finance, economics, environmental science, and biomedical engineering, aiding in forecasting, pattern identification, and understanding underlying mechanisms. While traditional time-domain methods focus on trends and seasonality, they often miss periodicities better captured in the frequency domain. Analyzing time series in the frequency domain uncovers spectral properties, offering deeper insights into underlying processes, aiding in differentiating data-generating processes of various populations, and assisting in classification. Common approaches use smoothed estimators, such as the smoothed periodogram, to minimize bias by averaging spectra from individual replicates within a population. However, these methods struggle with spectral variability among replicates, and abrupt values can skew estimators, complicating discrimination and classification. There's a gap in the literature for methods that account for within-population spectral variability, separate white noise effects from autocorrelations, and employ robust estimators in the presence of outliers. This paper fills that gap by introducing a robust framework for classifying time series groups. The process involves transforming time series into the frequency domain using the Fourier Transform, computing the power spectrum, and using the inverse Fourier Transform to obtain the cepstrum. To enhance spectral estimates' robustness and consistency, we apply the multitaper periodogram and the M-periodogram. These features are then used in Linear Discriminant Analysis (LDA) to improve classification accuracy and interpretability, offering a powerful tool for precise temporal pattern distinction and resilience to data anomalies.