Estimate of time series similarity based on models

Determining the measure as a distance between time series is a starting point for many data mining tasks such as clustering and classification. Clustering is a main method of teaching without a teacher, which is used to divide data into groups based on the internal and a priori unknown characteristics inherent in the data. When dividing data into clusters, the need arises to select the similarity metric between objects. The paper describes the main existing algorithms for the “distance” searching between time series, which describe well this problem for small time series and under the absence of outliers. Outliers inherent in real processes lead to improper clustering, and, consequently, to wrong decisions making. It is proposed to consider the distance between time series in the form of the distance between models (ARIMA) of these time series. In the presence of a large number of outliers, classical methods linearly increase the distances between time series, while the distance proposed in the article according to the models behaves as a logarithmic function. It is shown that with an increase in the number of measurements, the relative errors for all classical methods remain almost unchanged. At the same time, the relative error for estimating the distance by the models is much smaller and decreases with an increase in the number of measurements. The main achievement of the article is the determination of the distance between time series, based on the concept of a model, and the comparison of this distance with the corresponding classical methods most commonly used. Using the Monte Carlo method, it has been shown that the proposed distance is more resistant to outliers and gives more accurate results for time series with a large number of observations. In addition, the complexity of the algorithm for calculating distances based on models is less than the analogous computational complexity of existing algorithms (DTW, ERP, Euclidean distance). There is no doubt that the use of models is one of the most convenient tools for studying the similarity of processes. In addition, for analysis taking into account this algorithm, it is convenient to use the averaged evolutions and the limiting evolutions in the diffusion approximation scheme. Also, due to the resistance to outliers of limiting evolutions, the entered distance can be used in clustering to build more noise-resistant clusters. © 2019 by Begell House Inc.