A likelihood ratio distance measure for the similarity between the Fourier transform of time series

Fast Fourier Transforms (FFTs) have been a popular transformation and compression technique in time series data mining since first being proposed for use in this context in [1]. The Euclidean distance between coefficients has been the most commonly used distance metric with FFTs. However, on many problems it is not the best measure of similarity available. In this paper we describe an alternative distance measure based on the likelihood ratio statistic to test the hypothesis of difference between series. We compare the new distance measure to Euclidean distance on five types of data with varying levels of compression. We show that the likelihood ratio measure is better at discriminating between series from different models and grouping series from the same model.