Walsh Fourier Transform of Locally Stationary Time Series

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.