Path signature-based phase space reconstruction for stock trend prediction

In the field of quantitative finance, stock price trend prediction has always been one of the concerns of people. Stock price time series is the most important calculation basis in stock price prediction. The usual research idea is to take the one-dimensional single variable stock price time series to construct sample matrix through phase space reconstruction (PSR), and use it as the feature input of machine learning algorithm to predict the stock price. However, we often need a relatively large embedded dimension to obtain more useful information, which easily leads to the problems of high matrix dimension, over-fitting of prediction and low computational efficiency. To solve the above problems, we propose a path signature-based phase space reconstruction (PSR-PS) feature engineering approach for stock trend prediction, which can effectively extract features, reduce the dimension of high-dimensional price series data information and capture the necessary and effective information. Extensive experiments on several benchmark data sets from diverse real financial markets show that PSR-PS outperforms PSR and PSR-PCA (Principal component analysis-based PSR) in accuracy, precision and computational time, combined with different machine learning algorithms. It suggests that the proposed PSR-PS is effective.