The Relevance of Features to Limit Order Book Learning

The promising predictive power of machine learning (ML) models is encouraging a wide range of applications, but the weak interpretability of their black-box feature is a major obstacle to their application to finance. The large scale of limit order book (LOB) data provides fertile ground for ML implementation and exploration in finance. To examine the contribution of input elements to ML models, we propose three novel statistical measures for ranking each feature set from the LOB data and the combinations of feature sets: the $p$-value from hypothesis testing with a black-box model, a newly defined out-of-sample $R^2$ with respect to the objective function, and another new $R^2$ with respect to the classification score. Multiple measures are used to evaluate the level of significance of the features and their consistency. We empirically test several distinct models using LOB data from the Chinese A-share market. We find that feature relevance varies greatly across models for LOB forecasting. Moreover, notable patterns of consistency and significance offer important insights into the remarkable empirical performance of some black-box models. The testing results motivate us to improve prediction with ensemble learning. An additional sensitivity analysis clarifies that the feature rankings are robust to off-machine parameters under the well-designed deep convolutional neutral network