A pattern representation of stock time series based on DTW

Abstract

Time series analysis based on pattern discovery has received a lot of interests in the fields of economic physics and machine learning due to its simplicity and ability to reveal complex nonlinear behavior in stock market. Dynamic Time Warping (DTW) is a useful tool to extract morphological characteristics of time series for its capacity to cope with time shifts and warpings. In this paper, we propose a new time series representation method for stock time series based on dynamic time warping (DTW) called PR-DTW. A combinatorial optimization model with strict constraints is built to get the pattern representation of stock time series. To simplify the calculation, we construct another unconstrained global optimization problem whose optimal solution includes the optimal solution of the original combinatorial optimization problem based on a theorem proved in this paper. Particle Swarm Optimization algorithm is used to solve the global optimization problem, then the results can be converted into the optimal solution of the combinatorial optimization problem through a few simple formulas given in the theorem. The results of three classifiers (1NN, Decision Tree, Multi-layer Perceptron) implemented on 15 sectors in Chinese A-share market unanimously demonstrate that PR-DTW has the capability of extracting time series short-term patterns which is widely regarded as difficulty. And we conclude that PR-DTW has the capability of prevention of End Effect, anti-noise and segmentation. Moreover, by extracting the top ten patterns predicting stock’s rise and fall in short term (10 days) according to the ranking of stock’s rising probability in the next three days, we find out the short-term patterns obtained by PR-DTW have prospective directive to the stock trend analysis in short term.