Adaptive dissimilarity index for measuring time series proximity

The most widely used measures of time series proximity are the Euclidean distance and dynamic time warping. The latter can be derived from the distance introduced by Maurice Fréchet in 1906 to account for the proximity between curves. The major limitation of these proximity measures is that they are based on the closeness of the values regardless of the similarity w.r.t. the growth behavior of the time series. To alleviate this drawback we propose a new dissimilarity index, based on an automatic adaptive tuning function, to include both proximity measures w.r.t. values and w.r.t. behavior. A comparative numerical analysis between the proposed index and the classical distance measures is performed on the basis of two datasets: a synthetic dataset and a dataset from a public health study.