Discriminant analysis based on binary time series

• Published in: Metrika Vol. 83; no. 5; pp. 569 - 595
• Main Authors: Goto, Yuichi, Taniguchi, Masanobu
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2020; Springer Nature B.V
• Subjects: Asymptotic methods; Categories; Classification; Discriminant analysis; Economic Theory/Quantitative Economics/Mathematical Methods; Electrocardiography; Mathematics and Statistics; Outliers (statistics); Probability Theory and Stochastic Processes; Robustness; Stationary processes; Statistics; Time series; Discriminant analysis; Misclassification probability; Binary time series; 62H30; 62G86; Stationary process; Robustness; Spectral density
• ISSN: 0026-1335; 1435-926X
• DOI: 10.1007/s00184-019-00746-1

Binary time series can be derived from an underlying latent process. In this paper, we consider an ellipsoidal alpha mixing strictly stationary process and discuss the discriminant analysis and propose a classification method based on binary time series. Assume that the observations are generated by time series which belongs to one of two categories described by different spectra. We propose a method to classify into the correct category with high probability. First, we will show that the misclassification probability tends to zero when the number of observation tends to infinity, that is, the consistency of our discrimination method. Further, we evaluate the asymptotic misclassification probability when the two categories are contiguous. Finally, we show that our classification method based on binary time series has good robustness properties when the process is contaminated by an outlier, that is, our classification method is insensitive to the outlier. However, the classical method based on smoothed periodogram is sensitive to outliers. We also deal with a practical case where the two categories are estimated from the training samples. For an electrocardiogram data set, we examine the robustness of our method when observations are contaminated with an outlier.