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.

中文翻译：

---

基于二进制时间序列的判别分析

二进制时间序列可以从潜在的潜在过程中推导出来。在本文中，我们考虑了一个椭球 alpha 混合严格平稳过程，并讨论了判别分析，并提出了一种基于二进制时间序列的分类方法。假设观测值是由属于不同光谱描述的两个类别之一的时间序列生成的。我们提出了一种以高概率分类到正确类别的方法。首先，我们将证明当观察次数趋于无穷大时，误分类概率趋于零，即我们的判别方法的一致性。此外，当两个类别连续时，我们评估渐近错误分类概率。最后，我们表明，当过程受到异常值污染时，我们基于二进制时间序列的分类方法具有良好的鲁棒性，即我们的分类方法对异常值不敏感。然而，基于平滑周期图的经典方法对异常值很敏感。我们还处理了一个实际案例，其中两个类别是从训练样本中估计出来的。对于心电图数据集，当观察被异常值污染时，我们检查我们的方法的稳健性。