Experimental analysis of similarity measurements for multivariate time series and its application to the stock market

Similarity measurement takes on critical significance in strategies that seek similar stocks based on historical data to make predictions. Stock data refers to a multidimensional time series with features of non-linearity and high noise, posing a challenge to the practical design of similarity measurement. However, the existing similarity measurements cannot better address the negative effects of the singularity of data and correlations of data in multidimensional stock price series, such that the performance of stock prediction will be reduced. In this study, a novel method named dynamic multi-factor similarity measurement (DMFSM) is proposed to accurately describe the similarity between a pair of multidimensional time series. DMFSM is capable of eliminating effects exerted by singularity and correlations of data using dynamic time warping (DTW) with Mahalanobis distance embedded and weights of series nodes in multidimensional time series. To validate the efficiency of DMFSM, several experiments were performed on a total of 675 stocks, which comprised 290 stocks from the Shanghai Stock Exchange, 285 stocks from the Shenzhen Stock Exchange, as well as 100 stocks from the Growth Enterprise Market of the Shenzhen Stock Exchange. The experiment results for mean absolute error of predictions indicated that DMFSM (0.018) outperformed similarity measurements (e.g., Euclidean distance (0.023), DTW (0.054), and dynamic multi-perspective personalized similarity measurement (0.023)).