Time Series Averaging under Time Warping

Time Series such as sensor signals, speech or stock prices generally vary in length and speed. To cope with such temporal variations, warping distances such as Dynamic Time Warping (DTW) are often used. In recent years, the problem of finding an average of time series under DTW has been faced and many properties such as the existence, uniqueness, complexity, exact solutions and heuristic solutions have been studied. In practice, a DTW average may not ‘look like’ an averagely shaped curve of the sample time series. This is reasoned in the nature of the DTW distance itself. Therefore, several alternative warping distances have been proposed. However, as of today, they have rarely been used for computing average curves. The goal of this thesis it to explore the behavior of different warping distances for time series averaging. One challenge is to evaluate such averages quantitatively and qualitatively.