A new time‐frequency model and a method to classify time series data are proposed in this article. By viewing the observed signals as realizations of locally dyadic stationary (LDS) processes, a LDS model can be used to provide a time‐frequency decomposition of the signals, under which the evolutionary Walsh spectrum and related statistics can be defined and estimated. The classification procedure is as follows. First choose a training data set that comprises two groups of time series with a known group. Then compute the time frequency feature (the energy) using the training data set, and use a best tree method to maximize the discrepancy of this feature between the two groups. Finally, choose the testing data set with the unknown group as validation data, and use a discriminant statistic to classify the validation data to one of the groups. The classification method is illustrated via an electroencephalographic dataset and the Ericsson B transaction time dataset. The proposed classification method performs better for integer‐valued time series in terms of classification error rates in both simulations and real‐life applications.

中文翻译：

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局部平稳时间序列的 Walsh Fourier 变换

本文提出了一种新的时频模型和一种对时间序列数据进行分类的方法。通过将观察到的信号视为局部二元平稳 (LDS) 过程的实现，LDS 模型可用于提供信号的时频分解，在此分解下，可以定义和估计进化沃尔什谱和相关统计数据。分类程序如下。首先选择一个训练数据集，该数据集包含两组时间序列和一个已知组。然后使用训练数据集计算时频特征（能量），并使用最佳树方法最大化两组之间该特征的差异。最后，选择具有未知组的测试数据集作为验证数据，并使用判别统计将验证数据分类到其中一组。分类方法通过脑电图数据集和 Ericsson B 交易时间数据集进行说明。所提出的分类方法在模拟和实际应用中的分类错误率方面对整数值时间序列表现更好。